HDU5976 Detachment

/*
 HDU5976 Detachment
 http://acm.hdu.edu.cn/showproblem.php?pid=5976
 数论 等差数列
 *
 *
 */
#include <cstdio>
#include <algorithm>
#include <vector>
using namespace std;
const int mod=1000000007;
const int Nmax=50001;
vector<long long> v;
long long f[Nmax];
long long g[Nmax];
long long qpow(long long base,int n)
{
    long long ans=1LL;
    base=base%mod;
    while(n>0)
    {
        if(n&1)
            ans=ans*base%mod;
        base=(base*base)%mod;
        n>>=1;
    }
    while(ans<0)
        ans+=mod;
    return ans;
}

int main()
{
    //freopen("3.in","r",stdin);
    int t;
    scanf("%d",&t);
    long long x;
    f[1]=1LL;
     
    f[0]=0LL;
    f[2]=2LL;
    g[1]=1LL;
    g[2]=2LL;
    v.push_back(f[1]);
    v.push_back(f[2]);
    for(int i=3;i<Nmax;i++)
    {
        g[i]=1LL*i*g[i-1]%mod;
        f[i]=1LL*i+f[i-1];
        v.push_back(f[i]);
    }
    //printf("%lld
",f[Nmax-1]);
    while(t--)
    {
        long long ans=1LL;
        scanf("%lld",&x);
        int j=1;
        int k=1;
        for(int i=1;i<Nmax;i++)
        {
            if(x>=f[i] && x<f[i+1])
            {
                j=i;
                break;
            }
        }
        //printf("bj:%d
",j);
        j=lower_bound(v.begin(),v.end(),x)-v.begin();
        while(!(x>=f[j]&& x<f[j+1]))
            j++;
        //printf("j:%d
",j);
        long long remain=x-f[j];
        if(remain)
        {
            if(remain==j)
                k=2;
            else
                k=j+1-remain;
            //printf("j:%d k:%d
",j,k);
            ans=g[j];
            ans=ans*qpow(1LL*k, mod-2 )%mod;
            ans=ans*(k+remain)%mod;
        }
        else 
        {
            ans=g[j];
        }
        while(ans<0)
            ans+=mod;
        printf("%lld
",ans);
    }
    return 0;
}