#include <bits/stdc++.h>
using namespace std;
const int LIM = (1E9 + 7);
void calc(vector<long long> &pred, long long x, int c) {
  pred[0] = x;
  for (int i = 1; i < c; i++) {
    pred[i] = pred[i - 1] * pred[i - 1] % LIM;
  }
  return;
}
long long pow(vector<long long> &pred, long long x, long long n) {
  long long res = 0;
  int pos = 0;
  for (; n != 0; n = n >> 1) {
    if (n & 0x1 != 0) {
      long long cur = 1;
      for (int i = 0; pos >> i != 0; i++) {
        if (pos >> i & 0x1 != 0) {
          cur = cur * pred[i] % LIM;
        }
      }
      res = (res + cur) % LIM;
    }
    pos++;
  }
  return res;
}
int main() {
  int case_count;
  ios_base::sync_with_stdio(false), cin.tie(nullptr);
  cin >> case_count;
  for (int case_no = 0; case_no < case_count; case_no++) {
    long long b, k, c = 0;
    cin >> b >> k;
    for (long long tmp = k; tmp != 0; tmp = tmp >> 1) {
      c++;
    }
    vector<long long> pred(c);
    calc(pred, b, c);
    cout << pow(pred, b, k) << endl;
  }
  return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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;
const int LIM = (1E9 + 7);
void calc(vector<long long> &pred, long long x, int c) {
  pred[0] = x;
  for (int i = 1; i < c; i++) {
    pred[i] = pred[i - 1] * pred[i - 1] % LIM;
  }
  return;
}
long long pow(vector<long long> &pred, long long x, long long n) {
  long long res = 0;
  int pos = 0;
  for (; n != 0; n = n >> 1) {
    if (n & 0x1 != 0) {
      long long cur = 1;
      for (int i = 0; pos >> i != 0; i++) {
        if (pos >> i & 0x1 != 0) {
          cur = cur * pred[i] % LIM;
        }
      }
      res = (res + cur) % LIM;
    }
    pos++;
  }
  return res;
}
int main() {
  int case_count;
  ios_base::sync_with_stdio(false), cin.tie(nullptr);
  cin >> case_count;
  for (int case_no = 0; case_no < case_count; case_no++) {
    long long b, k, c = 0;
    cin >> b >> k;
    for (long long tmp = k; tmp != 0; tmp = tmp >> 1) {
      c++;
    }
    vector<long long> pred(c);
    calc(pred, b, c);
    cout << pow(pred, b, k) << endl;
  }
  return 0;
}

```