2019-2020 ACM-ICPC, Asia Xuzhou Regional Contest

A - Cat

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <unordered_map>
#include <vector>
#include <map>
#include <list>
#include <queue>
#include <cstring>
#include <cstdlib>
#include <ctime>
#include <cmath>
#include <stack>
#include <set>
#pragma GCC optimize(3 , "Ofast" , "inline")
using namespace std ;
#define ios ios::sync_with_stdio(false) , cin.tie(0) , cout.tie(0)
#define x first
#define y second
typedef long long ll ;
const double esp = 1e-6 , pi = acos(-1) ;
typedef pair<int , int> PII ;
const int N = 1e6 + 10 , INF = 0x3f3f3f3f , mod = 1e9 + 7;
ll in()
{
  ll x = 0 , f = 1 ;
  char ch = getchar() ;
  while(!isdigit(ch)) {if(ch == '-') f = -1 ; ch = getchar() ;}
  while(isdigit(ch)) x = x * 10 + ch - 48 , ch = getchar() ;
  return x * f ;
}
void work()
{
  ll l = in() , r = in() , s = in() ;
  if(r - l + 1 <= 4) {
    ll ans = -1 ;
    for(ll i = l ;i <= r ;i ++ )
     {
       ll res = 0 ;
       for(ll j = i ;j <= r ;j ++ ) {
          res ^= j ;
          if(res <= s) ans = max(ans , j - i + 1) ;
       }
     }
     cout << ans << endl ;
     return ;
  }
  if(l % 2) {
    ll rr ;
    for(ll i = r; i ;i --)
     {
       if((i - l) % 4 == 0)
        {
          rr = i ;
          break ;
        }
     }
  //   cout << rr << endl ;
     ll ans = rr - l ;
     if(l <= s) {
       ans ++ ;
     }

     ll res = 0 ;
     for(ll i = rr + 1 ; i <= r ;i ++ ) {
       res ^= i ;
       if(res <= s) {
         ans = max(ans , i - l) ;
       }
       if((res ^ l) <= s) {
         ans = max(ans , i - l + 1) ;
       }
    //   cout << i << " " << res << " " << (res ^ l) << " " << ans << endl ;
     }
     cout << ans << endl ;
  }
  else {
    for(ll i = r ; ;i --) {
      if((i - l + 1) % 4 == 0)  {

        ll ans = i - l + 1 ;
        ll res = 0 ;
        for(ll j = i + 1; j <= r ;j ++ ) {
          res ^= j ;
          if(res <= s)
           ans = max(ans , j - l + 1) ;
        }
        cout << ans << endl ;
        return ;
      }

    }
  }
  return ;
}
int main()
{
  int t = in() ;
  while(t --) work() ;
  return 0 ;
}
/*
*/

C - ❤️ numbers

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <unordered_map>
#include <vector>
#include <map>
#include <list>
#include <queue>
#include <cstring>
#include <cstdlib>
#include <ctime>
#include <cmath>
#include <stack>
#include <set>
#pragma GCC optimize(3 , "Ofast" , "inline")
using namespace std ;
#define ios ios::sync_with_stdio(false) , cin.tie(0) , cout.tie(0)
#define x first
#define y second
typedef long long ll ;
const double esp = 1e-6 , pi = acos(-1) ;
typedef pair<int , int> PII ;
const int N = 1e6 + 10 , INF = 0x3f3f3f3f , mod = 1e9 + 7;
ll in()
{
  ll x = 0 , f = 1 ;
  char ch = getchar() ;
  while(!isdigit(ch)) {if(ch == '-') f = -1 ; ch = getchar() ;}
  while(isdigit(ch)) x = x * 10 + ch - 48 , ch = getchar() ;
  return x * f ;
}
int prime[N] , vis[N] ;
void work()
{
  int l = in() , r = in() ;
  if(r - l + 1 >= 10000) puts("Yes") ;
  else {
    int tot = 0 ;
    for(int i = 2; i < N ;i ++ ) {
      if(!vis[i]) prime[++ tot] = i ;
      for(int j = 1; j <= tot && prime[j] * i < N ;j ++ ) {
        vis[i * prime[j]] = 1 ;
        if(i % prime[j] == 0) break ;
      }
    }
    int ans = 0 ;
    for(int i = l ;i <= r;i ++ ) {
      if(i < N && !vis[i]) ans ++ ;
      else if(i >= N) {
        int f = 1;
        for(int j = 1; j <= tot ;j ++ ) {
          if(i % prime[j] == 0) {
            f = 0 ;
            break ;
          }
        }
        if(f) ans ++ ;
      }
    }
    if(ans * 3 < r - l + 1) puts("Yes") ;
    else puts("No") ;
  }
  return ;
}
int main()
{
  int n = in() ;
  while(n --) work() ;
  return 0 ;
}
/*
*/

E - Multiply

#include <cstdio>
#include <cstdlib>
#include <ctime>
#include <cstring>
#include <algorithm>
#include <iostream>
const int S=20;
using namespace std;

typedef long long ll;
#define maxn 1000000

ll factor[maxn];
int tot;

ll muti_mod(ll a,ll b,ll c){    //返回(a*b) mod c,a,b,c<2^63
    a%=c;
    b%=c;
    ll ret=0;
    while (b){
        if (b&1){
            ret+=a;
            if (ret>=c) ret-=c;
        }
        a<<=1;
        if (a>=c) a-=c;
        b>>=1;
    }
    return ret;
}

ll pow_mod(ll x,ll n,ll mod){  //返回x^n mod c ,非递归版
    if (n==1) return x%mod;
    int bit[64],k=0;
    while (n){
        bit[k++]=n&1;
        n>>=1;
    }
    ll ret=1;
    for (k=k-1;k>=0;k--){
        ret=muti_mod(ret,ret,mod);
        if (bit[k]==1) ret=muti_mod(ret,x,mod);
    }
    return ret;
}

bool check(ll a,ll n,ll x,ll t){   //以a为基，n-1=x*2^t，检验n是不是合数
    ll ret=pow_mod(a,x,n),last=ret;
    for (int i=1;i<=t;i++){
        ret=muti_mod(ret,ret,n);
        if (ret==1 && last!=1 && last!=n-1) return 1;
        last=ret;
    }
    if (ret!=1) return 1;
    return 0;
}

bool Miller_Rabin(ll n){
    ll x=n-1,t=0;
    while ((x&1)==0) x>>=1,t++;
    bool flag=1;
    if (t>=1 && (x&1)==1){
        for (int k=0;k<S;k++){
            ll a=rand()%(n-1)+1;
            if (check(a,n,x,t)) {flag=1;break;}
            flag=0;
        }
    }
    if (!flag || n==2) return 0;
    return 1;
}

ll gcd(ll a,ll b){
    if (a==0) return 1;
    if (a<0) return gcd(-a,b);
    while (b){
        ll t=a%b; a=b; b=t;
    }
    return a;
}

ll Pollard_rho(ll x,ll c){
    ll i=1,x0=rand()%x,y=x0,k=2;
    while (1){
        i++;
        x0=(muti_mod(x0,x0,x)+c)%x;
        ll d=gcd(y-x0,x);
        if (d!=1 && d!=x){
            return d;
        }
        if (y==x0) return x;
        if (i==k){
            y=x0;
            k+=k;
        }
    }
}

void findfac(ll n){           //递归进行质因数分解N
    if (!Miller_Rabin(n)){
        factor[tot++] = n;
        return;
    }
    ll p=n;
    while (p>=n) p=Pollard_rho(p,rand() % (n-1) +1);
    findfac(p);
    findfac(n/p);
}
int idx = 0 ;
struct node
{
	ll val , num ;
	node() {}
	node(ll val , ll num) : val(val) , num(num) {} 
	bool operator<(const node &a) const 
	{
		val < a.val ;
	}
}fac[maxn];
ll b[maxn] ;
bool solve(ll n)
{
	if (!Miller_Rabin(n)) 
	 {
	 	fac[++ idx] = {n , 1} ;
	 }
	else{
            tot = 0;
            findfac(n);
            sort(factor , factor + tot) ;
            idx = 0 ;
            for(int i = 0 ; i < tot ;i ++)
             {
             	if(factor[i] != fac[idx].val) 
             	 fac[++ idx] = {factor[i] , 1};
             	else 
             	 fac[idx].num ++ ;
			 }
        }
}
ll get(ll n , ll p)
{
	ll res = 0 ;
	while(n)
	{
		res += n / p ;
		n /= p ;
	}
	return res ;
}
int main(){
    srand(time(NULL));
    int t;
    scanf("%d",&t);
    while (t--){
        ll n , x , y ;
        scanf("%lld%lld%lld",&n , &x , &y);
        idx = 0 ;
		solve(x) ;
		for(int j = 1; j <= idx ;j ++) b[j] = 0 ;
        for(int i = 1; i <= n ;i ++)
         {
         	ll p ;
         	scanf("%lld" , &p) ;
         	for(int j = 1 ;j <= idx ;j ++)
         	 	b[j] += get(p , fac[j].val)  ;
		 }
		ll minx = 0 ;
		for(int j = 1; j <= idx ;j ++)
		  b[j] = get(y , fac[j].val) - b[j] , minx = max(minx , b[j]);
		for(int j = 1; j <= idx ;j ++)
		 	if(b[j] > 0)
		 	 	minx = min(minx , b[j] / fac[j].num) ; 
		printf("%lld
" , minx) ;
    }
}

F - The Answer to the Ultimate Question of Life, The Universe, and Everything.

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <unordered_map>
#include <vector>
#include <map>
#include <list>
#include <queue>
#include <cstring>
#include <cstdlib>
#include <ctime>
#include <cmath>
#include <stack>
#include <set>
#pragma GCC optimize(3 , "Ofast" , "inline")
using namespace std ;
#define ios ios::sync_with_stdio(false) , cin.tie(0) , cout.tie(0)
#define x first
#define y second
typedef long long ll ;
const double esp = 1e-6 , pi = acos(-1) ;
typedef pair<int , int> PII ;
const int N = 1e6 + 10 , INF = 0x3f3f3f3f , mod = 1e9 + 7;
ll in()
{
  ll x = 0 , f = 1 ;
  char ch = getchar() ;
  while(!isdigit(ch)) {if(ch == '-') f = -1 ; ch = getchar() ;}
  while(isdigit(ch)) x = x * 10 + ch - 48 , ch = getchar() ;
  return x * f ;
}
int a[210][3] = {
  -5000 , 0 , 5000,
  -5000 , 1 , 5000,
  -4373 , -486 , 4375,
  -5 , 4 , 4,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  -637 , -205 , 644,
  -169 , 44 , 168,
  -5000 , 2 , 5000,
  -216 , -52 , 217,
  -650 , -353 , 683,
  -695 , -641 , 843,
  -11 , 7 , 10,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  -265 , -262 , 332,
  -4114 , -588 , 4118,
  -3331 , 2195 , 2977,
  -1373 , -1276 , 1671,
  -95 , 47 , 91,
  -2816 , -741 , 2833,
  -401 , -287 , 445,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  -10 , 8 , 8,
  -2683 , 1839 , 2357,
  -2107 , 237 , 2106,
  -5000 , 3 , 5000,
  -2268 , -249 , 2269,
  -233 , -69 , 235,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  -1555 , -244 , 1557,
  -1120 , -509 , 1154,
  -3223 , 2358 , 2731,
  -444 , -84 , 445,
  -27 , 16 , 25,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  -823 , -307 , 837,
  -7 , -5 , 8,
  -2369 , 1709 , 2025,
  -758 , -473 , 815,
  -141 , 49 , 139,
  -3950 , -1247 , 3991,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  -796 , 602 , 659,
  1061109567 , 1061109567 , 1061109567 ,
  -2370 , 1518 , 2141,
  -3885 , -648 , 3891,
  -3329 , 1837 , 3131,
  -672 , 505 , 559,
  -998 , 361 , 982,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  -1201 , -163 , 1202,
  -966 , 668 , 845,
  -2744 , -1561 , 2903,
  -161 , 102 , 146,
  -5000 , 4 , 5000,
  -929 , 403 , 903,
  1 , 1 , 4,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  -403 , 134 , 398,
  -2359 , 824 , 2325,
  -533 , 401 , 443,
  -432 , -104 , 434,
  -335 , -146 , 344,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  -2080 , -829 , 2123,
  -706 , -196 , 711,
  -1300 , -706 , 1366,
  -2368 , -1719 , 2638,
  -1317 , 847 , 1188,
  -3707 , 1315 , 3651,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  -4126 , -1972 , 4271,
  -1390 , -1282 , 1686,
  -2514 , 1953 , 2036,
  -1803 , 365 , 1798,
  -3389 , -2912 , 3992,
  -4052 , 861 , 4039,
  -248 , -98 , 253,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  -22 , 14 , 20,
  -3168 , -991 , 3200,
  -2101 , -1638 , 2391,
  -893 , -622 , 984,
  -1797 , -903 , 1870,
  -2327 , 319 , 2325,
  -239 , 118 , 229,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  -7 , -4 , 8,
  -2689 , -1165 , 2760,
  -1309 , 947 , 1117,
  -1165 , -948 , 1345,
  -2948 , 853 , 2924,
  1061109567 , 1061109567 , 1061109567 ,
  -4793 , -2312 , 4966,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  -12 , 8 , 11,
  -1906 , -757 , 1945,
  -896 , -555 , 962,
  -4328 , 383 , 4327,
  -3677 , -1673 , 3789,
  -2804 , 1219 , 2725,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  -37 , -16 , 38,
  -1 , 0 , 5,
  -5000 , 5 , 5000,
  -2212 , -419 , 2217,
  -4034 , -3881 , 4988,
  -3989 , -726 , 3997,
  -1580 , -1238 , 1801,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  -1 , 2 , 5,
  -399 , 167 , 389,
  -3013 , -1766 , 3203,
  -1351 , -629 , 1395,
  -1116 , 816 , 946,
  -758 , -428 , 801,
  -86 , -77 , 103,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  -139 , 104 , 116,
  -7 , -3 , 8,
  1061109567 , 1061109567 , 1061109567 ,
  -2746 , -2552 , 3342,
  -8 , -7 , 10,
  -327 , -263 , 376,
  -2366 , 1528 , 2131,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
  -367 , 260 , 317,
  -463 , 215 , 447,
  -805 , 486 , 741,
  -3736 , -695 , 3744,
  -2135 , -516 , 2145,
  -3693 , -1049 , 3721,
  1061109567 , 1061109567 , 1061109567 ,
  1061109567 , 1061109567 , 1061109567 ,
1061109567 , 1061109567 , 1061109567 ,
-1534 , 383 , 1526,
-3874 , -1654 , 3972,
-4767 , -2476 , 4980,
-4125 , -1417 , 4180,
-3423 , -2943 , 4033,
-66 , -59 , 79,
1061109567 , 1061109567 , 1061109567 ,
1061109567 , 1061109567 , 1061109567 ,
1061109567 , 1061109567 , 1061109567 ,
-802 , -574 , 890,
-1354 , -1012 , 1521,
-3834 , -2149 , 4047,
-1328 , 891 , 1178,
1061109567 , 1061109567 , 1061109567 ,
1061109567 , 1061109567 , 1061109567 ,
-335 , -170 , 349,
1061109567 , 1061109567 , 1061109567 ,
1061109567 , 1061109567 , 1061109567 ,
-1168 , -160 , 1169,
-13 , -10 , 15,
-2839 , 1503 , 2691,
1061109567 , 1061109567 , 1061109567 ,
-4874 , 974 , 4861,
-90 , -29 , 91,
-4889 , 976 , 4876,
1061109567 , 1061109567 , 1061109567 ,
1061109567 , 1061109567 , 1061109567 ,
-4 , 5 , 5,
-1885 , -1092 , 2000,
-1639 , 318 , 1635,
-1702 , -1403 , 1974,
-4812 , -593 , 4815,
-377 , -215 , 399,
-20 , 16 , 16,
1061109567 , 1061109567 , 1061109567 ,
1061109567 , 1061109567 , 1061109567 ,
1061109567 , 1061109567 , 1061109567 ,
-1057 , -579 , 1112,
-2867 , -1606 , 3026,
-3752 , -1347 , 3809,
-2208 , 508 , 2199,
-2318 , -638 , 2334,
};
int main()
{
  int t = in() ;
  while(t --)
   {
     int x = in() ;
     if(a[x][0] != INF) cout << a[x][0] << " " << a[x][1] << " " << a[x][2] << endl ;
     else puts("impossible") ;
   }
  return 0 ;
}
/*
*/

H - Yuuki and a problem

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <unordered_map>
#include <vector>
#include <map>
#include <list>
#include <queue>
#include <cstring>
#include <cstdlib>
#include <ctime>
#include <cmath>
#include <stack>
#include <set>
#pragma GCC optimize(3 , "Ofast" , "inline")
using namespace std ;
#define ios ios::sync_with_stdio(false) , cin.tie(0) , cout.tie(0)
#define x first
#define y second
typedef long long ll ;
const double esp = 1e-6 , pi = acos(-1) ;
typedef pair<int , int> PII ;
const int N = 2e5 + 10 , INF = 0x3f3f3f3f , mod = 1e9 + 7;
ll in()
{
  ll x = 0 , f = 1 ;
  char ch = getchar() ;
  while(!isdigit(ch)) {if(ch == '-') f = -1 ; ch = getchar() ;}
  while(isdigit(ch)) x = x * 10 + ch - 48 , ch = getchar() ;
  return x * f ;
}
int n , m = 2e5, q , a[N] , L[30][30] , R[30][30] , cl , cr ;
int lowbit(int x){return x & -x ;}
struct Seg{
  struct node{
    int ls , rs ;
    ll sum ;
    void init() {ls = rs = sum = 0 ;}
  }t[N * 100] ;
  int rt[N] , tot ;
  ll res ;
  int newnode(){
    ++ tot ;
    t[tot].init() ;
    return tot ;
  }
  void init() {memset(rt , 0 , sizeof rt) ; tot = 0 ;}
  void update(int &rt , int l , int r , int pos , int v) {
    if(!rt) rt = newnode() ;
    t[rt].sum += v ;
    if(l == r) return ;
    int mid = l + r >> 1 ;
    if(pos <= mid) update(t[rt].ls , l , mid , pos , v) ;
    else update(t[rt].rs , mid + 1 , r , pos , v) ;
  }
  void update(int x , int pos , int v){
    while(x <= n)
      update(rt[x] , 1 , m , pos , v) , x += lowbit(x) ;
  }
  void query(int dep , int l , int r , int ql , int qr){
    if(ql > qr) return ;
    if(ql <= l && r <= qr) {
      for(int i = 1; i <= cl ;i ++ ) res -= t[L[dep][i]].sum ;
      for(int i = 1; i <= cr ;i ++ ) res += t[R[dep][i]].sum ;
      return ;
    }
    int mid = l + r >> 1 ;
    if(ql <= mid) {
      for(int i = 1; i <= cl ;i ++ ) L[dep + 1][i] = t[L[dep][i]].ls ;
      for(int i = 1; i <= cr ;i ++ ) R[dep + 1][i] = t[R[dep][i]].ls ;
      query(dep + 1 , l , mid , ql , qr) ;
    }
    if(qr > mid) {
      for(int i = 1; i <= cl ;i ++ ) L[dep + 1][i] = t[L[dep][i]].rs ;
      for(int i = 1; i <= cr ;i ++ ) R[dep + 1][i] = t[R[dep][i]].rs ;
      query(dep + 1 , mid + 1 , r , ql , qr) ;
    }
  }
}seg;
int main()
{
  while(scanf("%d%d" , &n ,&q) != EOF) {
    for(int i = 1;i <= n ;i ++ ) scanf("%d" , &a[i]) ;
    seg.init() ;
    for(int i = 1; i <= n ;i ++ )
     seg.update(i , a[i] , a[i]) ;
    int op , x , y ;
    while(q --) {
      scanf("%d%d%d" , &op , &x , &y) ;
      if(op == 1) {
        seg.update(x , a[x] , -a[x]) ;
        a[x] = y ;
        seg.update(x , a[x] , a[x]) ;
      }else {
        x -- ;
        cl = 0 , cr = 0 ;
        for(int j = x ;j ;j -= lowbit(j)) L[0][++ cl] = seg.rt[j] ;
        for(int j = y ;j ;j -= lowbit(j)) R[0][++ cr] = seg.rt[j] ;
        ll l = 0 , r = 0 ;
        do{
          r = l + 1 ;
          seg.res = 0 ;
          seg.query(0 , 1 , m , 1 , min(1ll * m , r)) ;
          l = seg.res ;
        }while(l >= r) ;
        printf("%lld
" , l + 1) ;
      }
    }
  }
  return 0 ;
}
/*
*/

M - Kill the tree

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <unordered_map>
#include <vector>
#include <map>
#include <list>
#include <queue>
#include <cstring>
#include <cstdlib>
#include <ctime>
#include <cmath>
#include <stack>
#include <set>
#pragma GCC optimize(3 , "Ofast" , "inline")
using namespace std ;
#define ios ios::sync_with_stdio(false) , cin.tie(0) , cout.tie(0)
#define x first
#define y second
#define pb push_back
typedef long long ll ;
const double esp = 1e-6 , pi = acos(-1) ;
typedef pair<int , int> PII ;
const int N = 1e6 + 10 , INF = 0x3f3f3f3f , mod = 1e9 + 7;
ll in()
{
  ll x = 0 , f = 1 ;
  char ch = getchar() ;
  while(!isdigit(ch)) {if(ch == '-') f = -1 ; ch = getchar() ;}
  while(isdigit(ch)) x = x * 10 + ch - 48 , ch = getchar() ;
  return x * f ;
}
int n , size[N] , son[N] ;
vector<int> res[N] , v[N] ;
int fa[N] ;
void dfs(int u , int f){
  size[u] = 1 ;
  fa[u] = f ;
  for(auto x : v[u]) {
    if(x == f) continue ;
    dfs(x , u) ;
    size[u] += size[x] ;
    if(size[x] > size[son[u]])
     son[u] = x ;
  }
  if(size[u] == 1 || size[son[u]] < size[u] - size[son[u]]) {
    res[u].pb(u) ;
    return ;
  }
  for(auto x : res[son[u]]) {
       while(x != u && size[u] - size[x] > size[x]) x = fa[x] ;
       res[u].pb(x) ;
       if(x != u && size[u] - size[x] == size[x]) res[u].pb(fa[x]) ;
  }
  sort(res[u].begin() , res[u].end()) ;
  res[u].erase(unique(res[u].begin() , res[u].end()) , res[u].end()) ;
}
int main()
{
  n = in() ;
  for(int i = 1; i < n ;i ++ ) {
    int a = in() , b = in() ;
    v[a].pb(b) , v[b].pb(a) ;
  }
  dfs(1 , 0) ;
  for(int i = 1; i <= n ;i ++ ) {
    if(res[i].size() == 1)
     cout << res[i][0] << endl ;
    else cout << res[i][0] << " " << res[i][1] << endl ;
  }
  return 0 ;
}
/*
*/