#include <bits/stdc++.h>
using namespace std;
long long int binpow(long long int a, long long int b, long long int m) {
  a %= m;
  long long int res = 1;
  while (b > 0) {
    if (b & 1) res = res * a % m;
    a = a * a % m;
    b >>= 1;
  }
  return res;
}
double log_base2(double d) { return log2(d); }
double log_base2(double d);
double findl(int k) { return log_base2(k); }
double findl(int k);
long long int find(int num, int kay) {
  long long int x;
  double y;
  int z;
  y = floor((findl(kay)));
  if (kay == 1) {
    x = 1;
  } else if (y == (findl(kay))) {
    x = binpow(num, y, 1000000007);
  } else {
    z = binpow(2, y, 1000000007);
    long long int b;
    b = binpow(num, y, 1000000007);
    long long int d;
    d = find(num, kay - z);
    if (d > 1000000007) {
      d = d % 1000000007;
    }
    x = b + d;
    if (x > 1000000007) {
      x = x % 1000000007;
    }
  }
  return x;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  for (int i = 0; i < t; i++) {
    int n, k;
    cin >> n >> k;
    long long int ans;
    ans = find(n, k);
    cout << ans << endl;
  }
}

### Prompt

Create a solution in CPP for 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 int binpow(long long int a, long long int b, long long int m) {
  a %= m;
  long long int res = 1;
  while (b > 0) {
    if (b & 1) res = res * a % m;
    a = a * a % m;
    b >>= 1;
  }
  return res;
}
double log_base2(double d) { return log2(d); }
double log_base2(double d);
double findl(int k) { return log_base2(k); }
double findl(int k);
long long int find(int num, int kay) {
  long long int x;
  double y;
  int z;
  y = floor((findl(kay)));
  if (kay == 1) {
    x = 1;
  } else if (y == (findl(kay))) {
    x = binpow(num, y, 1000000007);
  } else {
    z = binpow(2, y, 1000000007);
    long long int b;
    b = binpow(num, y, 1000000007);
    long long int d;
    d = find(num, kay - z);
    if (d > 1000000007) {
      d = d % 1000000007;
    }
    x = b + d;
    if (x > 1000000007) {
      x = x % 1000000007;
    }
  }
  return x;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  for (int i = 0; i < t; i++) {
    int n, k;
    cin >> n >> k;
    long long int ans;
    ans = find(n, k);
    cout << ans << endl;
  }
}

```