Codeforces 438D The Child and Sequence

At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite sequence of Picks.

Fortunately, Picks remembers how to repair the sequence. Initially he should create an integer array a[1], a[2], ..., a[n]. Then he should perform a sequence of m operations. An operation can be one of the following:

1. Print operation l, r. Picks should write down the value of .
2. Modulo operation l, r, x. Picks should perform assignment a[i] = a[i] mod x for each i (l ≤ i ≤ r).
3. Set operation k, x. Picks should set the value of a[k] to x (in other words perform an assignment a[k] = x).

Can you help Picks to perform the whole sequence of operations?

Input

The first line of input contains two integer: n, m (1 ≤ n, m ≤ 10⁵). The second line contains n integers, separated by space: a[1], a[2], ..., a[n] (1 ≤ a[i] ≤ 10⁹) — initial value of array elements.

Each of the next m lines begins with a number type .

• If type = 1, there will be two integers more in the line: l, r (1 ≤ l ≤ r ≤ n), which correspond the operation 1.
• If type = 2, there will be three integers more in the line: l, r, x (1 ≤ l ≤ r ≤ n; 1 ≤ x ≤ 10⁹), which correspond the operation 2.
• If type = 3, there will be two integers more in the line: k, x (1 ≤ k ≤ n; 1 ≤ x ≤ 10⁹), which correspond the operation 3.

Output

For each operation 1, please print a line containing the answer. Notice that the answer may exceed the 32-bit integer.

Examples

Input

5 5 1 2 3 4 5 2 3 5 4 3 3 5 1 2 5 2 1 3 3 1 1 3

Output

8 5

Input

10 10 6 9 6 7 6 1 10 10 9 5 1 3 9 2 7 10 9 2 5 10 8 1 4 7 3 3 7 2 7 9 9 1 2 4 1 6 6 1 5 9 3 1 10

Output

49 15 23 1 9

Note

Consider the first testcase:

• At first, a = {1, 2, 3, 4, 5}.
• After operation 1, a = {1, 2, 3, 0, 1}.
• After operation 2, a = {1, 2, 5, 0, 1}.
• At operation 3, 2 + 5 + 0 + 1 = 8.
• After operation 4, a = {1, 2, 2, 0, 1}.
• At operation 5, 1 + 2 + 2 = 5.

---

　　题目大意 维护一个数列，有3种操作，分别是区间求和，区间取模和单点修改。

　　显然线段树(请不要问我为什么。。。学长的Tag打在那儿的)

　　区间求和和单点修改都是线段树的拿手好戏，但是对于区间取模似乎不是那么好做。考虑可以区间批量更新sum吗？显然不行。

　　但是考虑到这里只有单点修改，而且对一个大于模数的数取模，它的值至多为它原来的值的一半。

　　所以区间记录一个最大值剪枝，每次区间取模先判断是否有必要进行递归取模，如果有，就暴力递归下去，在底层修改。

Code

/**
 * Codeforces
 * Problem#438D
 * Accepted
 * Time: 436ms
 * Memory: 8740k
 */
#include <bits/stdc++.h>
#ifndef WIN32
#define Auto "%lld"
#else
#define Auto "%I64d"
#endif
using namespace std;

typedef class SegTreeNode {
    public:
        int maxv;
        long long sum;
        SegTreeNode *l, *r;
        
        SegTreeNode():maxv(0), sum(0), l(NULL), r(NULL) {        }
        
        inline void pushUp() {
            maxv = max(l->maxv, r->maxv);
            sum = l->sum + r->sum; 
        }
}SegTreeNode;

typedef class SegTree {
    public:
        SegTreeNode* root;
        
        SegTree():root(NULL) {        }
        SegTree(int n, int* a) {
            build(root, 1, n, a);
        }
        
        void build(SegTreeNode*& node, int l, int r, int* a) {
            node = new SegTreeNode();
            if(l == r) {
                node->sum = node->maxv = a[l];
                return;
            }
            int mid = (l + r) >> 1;
            build(node->l, l, mid, a);
            build(node->r, mid + 1, r, a);
            node->pushUp();
        }
        
        void update(SegTreeNode*& node, int l, int r, int idx, int val) {
            if(l == r) {
                node->maxv = node->sum = val;
                return;
            }
            int mid = (l + r) >> 1;
            if(idx <= mid)    update(node->l, l, mid, idx, val);
            else update(node->r, mid + 1, r, idx, val);
            node->pushUp();
        }
        
        void update(SegTreeNode*& node, int l, int r, int ql, int qr, int moder) {
            if(l == r) {
                node->maxv = (node->sum %= moder);
                return;
            }
            int mid = (l + r) >> 1;
            if(qr <= mid && node->l->maxv >= moder)    update(node->l, l, mid, ql, qr, moder);
            else if(ql > mid && node->r->maxv >= moder)    update(node->r, mid + 1, r, ql, qr, moder);
            else if(qr > mid && ql <= mid) {
                if(node->l->maxv >= moder)
                    update(node->l, l, mid, ql, mid, moder);
                if(node->r->maxv >= moder)
                    update(node->r, mid + 1, r, mid + 1, qr, moder);
            }
            node->pushUp();
        }
        
        long long query(SegTreeNode*& node, int l, int r, int ql, int qr) {
            if(l == ql && r == qr) {
                return node->sum;
            }
            int mid = (l + r) >> 1;
            if(qr <= mid)    return query(node->l, l, mid, ql, qr);
            if(ql > mid)    return query(node->r, mid + 1, r, ql, qr);
                return query(node->l, l, mid, ql, mid) + query(node->r, mid + 1, r, mid + 1, qr);
            }              
}SegTree;              
                       
int n, m;              
int* arr;              
SegTree st;            
inline void init() {
    scanf("%d%d", &n, &m);
    arr = new int[(n + 1)];
    for(int i = 1; i <= n; i++)
        scanf("%d", arr + i);
    st = SegTree(n, arr);
}                      

inline void solve() {
    int opt, a, b, c;
    while(m--) {
        scanf("%d%d%d", &opt, &a, &b);
        if(opt == 1) {
            printf(Auto"
", st.query(st.root, 1, n, a, b));
        } else if(opt == 2) {
            scanf("%d", &c);
            st.update(st.root, 1, n, a, b, c);
        } else {
            st.update(st.root, 1, n, a, b);
        }
    }
}

int main() {
    init();
    solve();
    return 0;
}