#include <bits/stdc++.h>
using namespace std;
long long LOL = 1e9 + 7;
long long power(long long a, long long b) {
  a %= LOL;
  long long res = 1;
  while (b > 0) {
    if (b & 1) res = res * a % LOL;
    a = a * a % LOL;
    b >>= 1;
  }
  return res;
}
int main() {
  int t;
  cin >> t;
  for (int i = 1; i <= t; i++) {
    long long n;
    long long k;
    long long sol = 0;
    cin >> n >> k;
    string arr = bitset<32>(k).to_string();
    reverse(arr.begin(), arr.end());
    for (int i = 0; i < 32; i++) {
      if (arr[i] == '1') {
        sol = (sol + power(n, i)) % LOL;
      }
    }
    cout << sol << endl;
  }
  return 0;
}

### Prompt

Your challenge is to write a CPP solution 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;
long long LOL = 1e9 + 7;
long long power(long long a, long long b) {
  a %= LOL;
  long long res = 1;
  while (b > 0) {
    if (b & 1) res = res * a % LOL;
    a = a * a % LOL;
    b >>= 1;
  }
  return res;
}
int main() {
  int t;
  cin >> t;
  for (int i = 1; i <= t; i++) {
    long long n;
    long long k;
    long long sol = 0;
    cin >> n >> k;
    string arr = bitset<32>(k).to_string();
    reverse(arr.begin(), arr.end());
    for (int i = 0; i < 32; i++) {
      if (arr[i] == '1') {
        sol = (sol + power(n, i)) % LOL;
      }
    }
    cout << sol << endl;
  }
  return 0;
}

```