​​传送门​​ Given an array a of length n, you can do at most k operations of the following type on it:

choose 2 different elements in the array, add 1 to the first, and subtract 1 from the second. However, all the elements of a have to remain non-negative after this operation.
What is lexicographically the smallest array you can obtain?

An array x is lexicographically smaller than an array y if there exists an index i such that xi<yi, and xj=yj for all 1≤j<i. Less formally, at the first index i in which they differ, xi<yi.

Input

The first line contains an integer t (1≤t≤20) – the number of test cases you need to solve.

The first line of each test case contains 2 integers n and k (2≤n≤100, 1≤k≤10000) — the number of elements in the array and the maximum number of operations you can make.

The second line contains n space-separated integers a1, a2, …, an (0≤ai≤100) — the elements of the array a.

Output

For each test case, print the lexicographically smallest array you can obtain after at most k operations.

#include<bits/stdc++.h>
using namespace std;
const int inf = 0x3f3f3f3f;
#define ll long long     
const int mod = 1e9+7;
int a[110];

int main()
{
  int t;
  cin>>t;
  while(t--)
  {
    memset(a,0,sizeof(a));
    int n,k;
    cin>>n>>k;
    for(int i = 1; i <= n; i++)
    {
      cin>>a[i];
    }
    for(int i = 1; i < n; i++)
    {
      if(k >= a[i])
      {
        a[n] += a[i];
        k -= a[i];
        a[i] = 0;
      }
      else
      {
        a[n] += k;
        a[i] -= k;
        k = 0;
      }
    }
    for(int i = 1; i <= n; i++)
    {
      printf("%d ",a[i]);
    }
    cout<<endl;
  }
}