#include <bits/stdc++.h>
using namespace std;
const int MS = 1000001;
const long long int INF = 1e9 + 7;
void usaco(string filename) {
  string in = filename + ".in", out = filename + ".out";
  freopen(in.c_str(), "r", stdin);
  freopen(out.c_str(), "w", stdout);
}
template <class T>
bool comp(T a, T b) {
  if (a < b) return true;
  return false;
}
long long int po(long long int b, long long int p) {
  long long int ans = 1;
  while (p) {
    if (p % 2 == 0) {
      b = (b * b) % INF;
      p = p / 2;
    } else {
      ans = (ans * b) % INF;
      p--;
    }
  }
  return ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  while (t--) {
    long long int n, k;
    cin >> n >> k;
    long long int ans = 0;
    long long int cnt = 0, her = log2(k);
    while (cnt <= her + 1) {
      if (k & (1 << cnt)) ans += po(n, cnt);
      cnt++;
      ans %= INF;
    }
    cout << ans % INF << "\n";
  }
}

### Prompt

Generate 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;
const int MS = 1000001;
const long long int INF = 1e9 + 7;
void usaco(string filename) {
  string in = filename + ".in", out = filename + ".out";
  freopen(in.c_str(), "r", stdin);
  freopen(out.c_str(), "w", stdout);
}
template <class T>
bool comp(T a, T b) {
  if (a < b) return true;
  return false;
}
long long int po(long long int b, long long int p) {
  long long int ans = 1;
  while (p) {
    if (p % 2 == 0) {
      b = (b * b) % INF;
      p = p / 2;
    } else {
      ans = (ans * b) % INF;
      p--;
    }
  }
  return ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  while (t--) {
    long long int n, k;
    cin >> n >> k;
    long long int ans = 0;
    long long int cnt = 0, her = log2(k);
    while (cnt <= her + 1) {
      if (k & (1 << cnt)) ans += po(n, cnt);
      cnt++;
      ans %= INF;
    }
    cout << ans % INF << "\n";
  }
}

```