#include <bits/stdc++.h>
using namespace std;
const int N = 4e4 + 5;
long long T, n, b[N], c[N];
long long l, r, mid, mm;
long long check(long long mid) {
  long long cnt = 0;
  for (int i = 1; i <= n; i++) cnt += (mid - c[i]) / (n) * (n - i + 1);
  return b[n] - cnt;
}
int main() {
  cin >> T;
  while (T--) {
    cin >> n;
    for (int i = 1; i <= n; i++) cin >> b[i];
    for (int i = 2; i <= n; i++) c[i] = b[i] - b[i - 1];
    c[1] = b[1] - b[n];
    bool flag = false;
    for (int i = 2; i <= n; i++)
      if ((c[i] % n + n) % n != (c[i - 1] % n + n) % n) flag = true;
    if (flag) {
      puts("NO");
      continue;
    }
    l = 0, r = 1e9 + 5;
    while (l < r - 1) {
      mm = (l + r) >> 1;
      mid = c[1] + n * mm;
      long long t = check(mid);
      if (t == 0) {
        flag = true;
        break;
      } else if (t < 0)
        r = mm;
      else
        l = mm;
    }
    if (flag) {
      for (int i = 1; i <= n; i++)
        if (mid <= c[i]) flag = false;
      if (!flag) {
        puts("NO");
        continue;
      }
      puts("YES");
      for (int i = 1; i <= n; i++) cout << (mid - c[i]) / (n) << ' ';
      puts("");
    } else
      puts("NO");
  }
  return 0;
}

### Prompt

Please formulate a Cpp solution to the following problem:

n towns are arranged in a circle sequentially. The towns are numbered from 1 to n in clockwise order. In the i-th town, there lives a singer with a repertoire of a_i minutes for each i ∈ [1, n].

Each singer visited all n towns in clockwise order, starting with the town he lives in, and gave exactly one concert in each town. In addition, in each town, the i-th singer got inspired and came up with a song that lasts a_i minutes. The song was added to his repertoire so that he could perform it in the rest of the cities.

Hence, for the i-th singer, the concert in the i-th town will last a_i minutes, in the (i + 1)-th town the concert will last 2 ⋅ a_i minutes, ..., in the ((i + k) mod n + 1)-th town the duration of the concert will be (k + 2) ⋅ a_i, ..., in the town ((i + n - 2) mod n + 1) — n ⋅ a_i minutes.

You are given an array of b integer numbers, where b_i is the total duration of concerts in the i-th town. Reconstruct any correct sequence of positive integers a or say that it is impossible.

Input

The first line contains one integer t (1 ≤ t ≤ 10^3) — the number of test cases. Then the test cases follow.

Each test case consists of two lines. The first line contains a single integer n (1 ≤ n ≤ 4 ⋅ 10^4) — the number of cities. The second line contains n integers b_1, b_2, ..., b_n (1 ≤ b_i ≤ 10^{9}) — the total duration of concerts in i-th city.

The sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, print the answer as follows:

If there is no suitable sequence a, print NO. Otherwise, on the first line print YES, on the next line print the sequence a_1, a_2, ..., a_n of n integers, where a_i (1 ≤ a_i ≤ 10^{9}) is the initial duration of repertoire of the i-th singer. If there are multiple answers, print any of them.

Example

Input


4
3
12 16 14
1
1
3
1 2 3
6
81 75 75 93 93 87


Output


YES
3 1 3 
YES
1 
NO
YES
5 5 4 1 4 5 

Note

Let's consider the 1-st test case of the example:

  1. the 1-st singer in the 1-st city will give a concert for 3 minutes, in the 2-nd — for 6 minutes, in the 3-rd — for 9 minutes; 
  2. the 2-nd singer in the 1-st city will give a concert for 3 minutes, in the 2-nd — for 1 minute, in the 3-rd - for 2 minutes; 
  3. the 3-rd singer in the 1-st city will give a concert for 6 minutes, in the 2-nd — for 9 minutes, in the 3-rd — for 3 minutes. 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int N = 4e4 + 5;
long long T, n, b[N], c[N];
long long l, r, mid, mm;
long long check(long long mid) {
  long long cnt = 0;
  for (int i = 1; i <= n; i++) cnt += (mid - c[i]) / (n) * (n - i + 1);
  return b[n] - cnt;
}
int main() {
  cin >> T;
  while (T--) {
    cin >> n;
    for (int i = 1; i <= n; i++) cin >> b[i];
    for (int i = 2; i <= n; i++) c[i] = b[i] - b[i - 1];
    c[1] = b[1] - b[n];
    bool flag = false;
    for (int i = 2; i <= n; i++)
      if ((c[i] % n + n) % n != (c[i - 1] % n + n) % n) flag = true;
    if (flag) {
      puts("NO");
      continue;
    }
    l = 0, r = 1e9 + 5;
    while (l < r - 1) {
      mm = (l + r) >> 1;
      mid = c[1] + n * mm;
      long long t = check(mid);
      if (t == 0) {
        flag = true;
        break;
      } else if (t < 0)
        r = mm;
      else
        l = mm;
    }
    if (flag) {
      for (int i = 1; i <= n; i++)
        if (mid <= c[i]) flag = false;
      if (!flag) {
        puts("NO");
        continue;
      }
      puts("YES");
      for (int i = 1; i <= n; i++) cout << (mid - c[i]) / (n) << ' ';
      puts("");
    } else
      puts("NO");
  }
  return 0;
}

```