#include <bits/stdc++.h>
using namespace std;
long long constexpr max_n = 1e5 + 10, max_lg = 30, mas_sq = 1000, mod = 1e9 + 7;
long long bpow(long long x, long long y) {
  long long res = 1LL;
  while (y) {
    if (y & 1) {
      res *= x;
      res %= mod;
    }
    x *= x;
    x %= mod;
    y /= 2;
  }
  return res;
}
int32_t main() {
  ios::sync_with_stdio(false), cin.tie(nullptr);
  long long t = 1;
  cin >> t;
  while (t--) {
    long long n, k;
    cin >> n >> k;
    long long ans = 0LL;
    while (k > 0) {
      long long a = 0;
      for (long long i = 1; i <= k; i++) {
        if (((1LL << i) - 1LL) <= k) {
          a = i;
        } else
          break;
      }
      k -= ((1LL << a) - 1LL);
      if (k > 0) {
        ans += bpow(n, a);
        k--;
      } else {
        for (long long i = 0; i <= (a - 1); i++) {
          ans += bpow(n, i);
          ans %= mod;
        }
      }
      ans %= mod;
    }
    cout << (long long)ans << '\n';
  }
}

### Prompt

In cpp, your task is to solve 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 constexpr max_n = 1e5 + 10, max_lg = 30, mas_sq = 1000, mod = 1e9 + 7;
long long bpow(long long x, long long y) {
  long long res = 1LL;
  while (y) {
    if (y & 1) {
      res *= x;
      res %= mod;
    }
    x *= x;
    x %= mod;
    y /= 2;
  }
  return res;
}
int32_t main() {
  ios::sync_with_stdio(false), cin.tie(nullptr);
  long long t = 1;
  cin >> t;
  while (t--) {
    long long n, k;
    cin >> n >> k;
    long long ans = 0LL;
    while (k > 0) {
      long long a = 0;
      for (long long i = 1; i <= k; i++) {
        if (((1LL << i) - 1LL) <= k) {
          a = i;
        } else
          break;
      }
      k -= ((1LL << a) - 1LL);
      if (k > 0) {
        ans += bpow(n, a);
        k--;
      } else {
        for (long long i = 0; i <= (a - 1); i++) {
          ans += bpow(n, i);
          ans %= mod;
        }
      }
      ans %= mod;
    }
    cout << (long long)ans << '\n';
  }
}

```