#include <bits/stdc++.h>
using namespace std;
int main(int argc, const char* argv[]) {
  int t;
  cin >> t;
  while (t--) {
    long long n, k;
    cin >> n >> k;
    queue<bool> q;
    long long two_degree = 2;
    while (k) {
      if (k % two_degree != 0)
        q.push(true);
      else
        q.push(false);
      k -= k % two_degree;
      two_degree <<= 1;
    }
    long long result = 0;
    long long n_degree = 1;
    while (!q.empty()) {
      if (q.front()) result += n_degree;
      n_degree *= n;
      n_degree %= 1000000007;
      result %= 1000000007;
      q.pop();
    }
    cout << result << endl;
  }
}

### Prompt

Please create a solution in cpp to the following problem:

Theofanis really likes sequences of positive integers, thus his teacher (Yeltsa Kcir) gave him a problem about a sequence that consists of only special numbers.

Let's call a positive number special if it can be written as a sum of different non-negative powers of n. For example, for n = 4 number 17 is special, because it can be written as 4^0 + 4^2 = 1 + 16 = 17, but 9 is not.

Theofanis asks you to help him find the k-th special number if they are sorted in increasing order. Since this number may be too large, output it modulo 10^9+7.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The first and only line of each test case contains two integers n and k (2 ≤ n ≤ 10^9; 1 ≤ k ≤ 10^9).

Output

For each test case, print one integer — the k-th special number in increasing order modulo 10^9+7.

Example

Input


3
3 4
2 12
105 564


Output


9
12
3595374

Note

For n = 3 the sequence is [1,3,4,9...]

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int main(int argc, const char* argv[]) {
  int t;
  cin >> t;
  while (t--) {
    long long n, k;
    cin >> n >> k;
    queue<bool> q;
    long long two_degree = 2;
    while (k) {
      if (k % two_degree != 0)
        q.push(true);
      else
        q.push(false);
      k -= k % two_degree;
      two_degree <<= 1;
    }
    long long result = 0;
    long long n_degree = 1;
    while (!q.empty()) {
      if (q.front()) result += n_degree;
      n_degree *= n;
      n_degree %= 1000000007;
      result %= 1000000007;
      q.pop();
    }
    cout << result << endl;
  }
}

```