#include <bits/stdc++.h>
using namespace std;
int gcd(int a, int b) {
  if (b == 0) {
    return a;
  }
  return gcd(b, a % b);
}
int lcm(int a, int b) { return (a * b) / gcd(a, b); }
int binarySearch(int arr[], int l, int r, int x) {
  while (l <= r) {
    int m = l + (r - l) / 2;
    if (arr[m] == x) {
      return m;
    }
    if (arr[m] < x) {
      l = m + 1;
    } else {
      r = m - 1;
    }
  }
  return -1;
}
long long int binomialCoeff(long long int n, long long int k) {
  long long int res = 1, i;
  if (k > n - k) k = n - k;
  for (i = 0; i < k; ++i) {
    res *= (n - i);
    res /= (i + 1);
  }
  return res;
}
int findMinDiff(vector<int> ar, int a[]) {
  std::vector<int> arr;
  for (int i = 0; i < ar.size(); ++i) {
    arr.push_back(a[ar[i]]);
  }
  sort(arr.begin(), arr.end());
  int n = arr.size();
  int diff = INT_MAX;
  for (int i = 0; i < n - 1; i++)
    if (arr[i + 1] - arr[i] < diff) diff = arr[i + 1] - arr[i];
  return diff;
}
int power(int x, unsigned int y, int p) {
  int res = 1;
  x = x % p;
  if (x == 0) return 0;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int t;
  cin >> t;
  while (t--) {
    long long int n, k, i, j;
    cin >> n >> k;
    long long int a[n], z = 0;
    map<long long int, long long int> m;
    std::vector<long long int> v;
    for (i = 0; i < n; ++i) {
      cin >> a[i];
      if (a[i] % k != 0) {
        int xx = k - (a[i] % k);
        v.push_back(xx);
      }
    }
    sort(v.begin(), v.end());
    int q = 0;
    if (v.size() == 0) {
      cout << "0\n";
      continue;
    }
    m[v[0]] = 1;
    for (int i = 1; i < v.size(); ++i) {
      if (v[i] == v[i - 1]) {
        q++;
        m[k * q + v[i]] = 1;
      } else {
        m[v[i]] = 1;
        q = 0;
      }
    }
    long long int ans = 0, temp = 0;
    for (auto i : m) {
      ans += i.first - temp;
      temp = i.first;
    }
    if (ans != 0) {
      ans++;
    }
    cout << ans << endl;
  }
  return 0;
}

### Prompt

Your task is to create a cpp solution to the following problem:

You are given an array a consisting of n positive integers.

Initially, you have an integer x = 0. During one move, you can do one of the following two operations:

  1. Choose exactly one i from 1 to n and increase a_i by x (a_i := a_i + x), then increase x by 1 (x := x + 1). 
  2. Just increase x by 1 (x := x + 1). 



The first operation can be applied no more than once to each i from 1 to n.

Your task is to find the minimum number of moves required to obtain such an array that each its element is divisible by k (the value k is given).

You have to answer t independent test cases. 

Input

The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.

The first line of the test case contains two integers n and k (1 ≤ n ≤ 2 ⋅ 10^5; 1 ≤ k ≤ 10^9) — the length of a and the required divisior. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is the i-th element of a.

It is guaranteed that the sum of n does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — the minimum number of moves required to obtain such an array that each its element is divisible by k.

Example

Input


5
4 3
1 2 1 3
10 6
8 7 1 8 3 7 5 10 8 9
5 10
20 100 50 20 100500
10 25
24 24 24 24 24 24 24 24 24 24
8 8
1 2 3 4 5 6 7 8


Output


6
18
0
227
8

Note

Consider the first test case of the example:

  1. x=0, a = [1, 2, 1, 3]. Just increase x; 
  2. x=1, a = [1, 2, 1, 3]. Add x to the second element and increase x; 
  3. x=2, a = [1, 3, 1, 3]. Add x to the third element and increase x; 
  4. x=3, a = [1, 3, 3, 3]. Add x to the fourth element and increase x; 
  5. x=4, a = [1, 3, 3, 6]. Just increase x; 
  6. x=5, a = [1, 3, 3, 6]. Add x to the first element and increase x; 
  7. x=6, a = [6, 3, 3, 6]. We obtained the required array. 



Note that you can't add x to the same element more than once.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int gcd(int a, int b) {
  if (b == 0) {
    return a;
  }
  return gcd(b, a % b);
}
int lcm(int a, int b) { return (a * b) / gcd(a, b); }
int binarySearch(int arr[], int l, int r, int x) {
  while (l <= r) {
    int m = l + (r - l) / 2;
    if (arr[m] == x) {
      return m;
    }
    if (arr[m] < x) {
      l = m + 1;
    } else {
      r = m - 1;
    }
  }
  return -1;
}
long long int binomialCoeff(long long int n, long long int k) {
  long long int res = 1, i;
  if (k > n - k) k = n - k;
  for (i = 0; i < k; ++i) {
    res *= (n - i);
    res /= (i + 1);
  }
  return res;
}
int findMinDiff(vector<int> ar, int a[]) {
  std::vector<int> arr;
  for (int i = 0; i < ar.size(); ++i) {
    arr.push_back(a[ar[i]]);
  }
  sort(arr.begin(), arr.end());
  int n = arr.size();
  int diff = INT_MAX;
  for (int i = 0; i < n - 1; i++)
    if (arr[i + 1] - arr[i] < diff) diff = arr[i + 1] - arr[i];
  return diff;
}
int power(int x, unsigned int y, int p) {
  int res = 1;
  x = x % p;
  if (x == 0) return 0;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int t;
  cin >> t;
  while (t--) {
    long long int n, k, i, j;
    cin >> n >> k;
    long long int a[n], z = 0;
    map<long long int, long long int> m;
    std::vector<long long int> v;
    for (i = 0; i < n; ++i) {
      cin >> a[i];
      if (a[i] % k != 0) {
        int xx = k - (a[i] % k);
        v.push_back(xx);
      }
    }
    sort(v.begin(), v.end());
    int q = 0;
    if (v.size() == 0) {
      cout << "0\n";
      continue;
    }
    m[v[0]] = 1;
    for (int i = 1; i < v.size(); ++i) {
      if (v[i] == v[i - 1]) {
        q++;
        m[k * q + v[i]] = 1;
      } else {
        m[v[i]] = 1;
        q = 0;
      }
    }
    long long int ans = 0, temp = 0;
    for (auto i : m) {
      ans += i.first - temp;
      temp = i.first;
    }
    if (ans != 0) {
      ans++;
    }
    cout << ans << endl;
  }
  return 0;
}

```