#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize("O3", "unroll-loops")
long long mod = 1e9 + 7;
void solve();
void tests() {
  long long test;
  cin >> test;
  while (test--) {
    solve();
  }
}
long long power(long long x, unsigned long long y, long long p) {
  long long res = 1;
  x = x % p;
  if (x == 0) return 0;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
void io_files() {}
int32_t main() {
  ;
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  ;
  cout << fixed << setprecision(20);
  ;
  if (1) io_files();
  if (1)
    tests();
  else
    solve();
}
void solve() {
  long long n, k;
  cin >> n >> k;
  long long ans = 0;
  for (long long i = 0; i < 32; i++) {
    if ((1 << i) & k) ans += power(n, i, mod);
    ans %= mod;
  }
  cout << ans << endl;
}

### 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;
#pragma GCC optimize("O3", "unroll-loops")
long long mod = 1e9 + 7;
void solve();
void tests() {
  long long test;
  cin >> test;
  while (test--) {
    solve();
  }
}
long long power(long long x, unsigned long long y, long long p) {
  long long res = 1;
  x = x % p;
  if (x == 0) return 0;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
void io_files() {}
int32_t main() {
  ;
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  ;
  cout << fixed << setprecision(20);
  ;
  if (1) io_files();
  if (1)
    tests();
  else
    solve();
}
void solve() {
  long long n, k;
  cin >> n >> k;
  long long ans = 0;
  for (long long i = 0; i < 32; i++) {
    if ((1 << i) & k) ans += power(n, i, mod);
    ans %= mod;
  }
  cout << ans << endl;
}

```