Problem: <image>

To monitor cryptocurrency exchange rates trader William invented a wonderful device consisting of n lights arranged in a row. The device functions in the following way:

Initially, all lights on William's device are turned off. At the beginning of a new iteration the device randomly, with a uniform distribution, picks a light that is turned off and turns it on, telling William which cryptocurrency he should invest in. After this iteration if any k consecutive lights contain more than one turned on light, then the device finishes working.

William doesn't like uncertainty, so he wants you to calculate the expected value of the number of lights that are turned on in the device after it finishes working.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10). Description of the test cases follows.

The only line for each test case contains two integers n and k (2 ≤ k ≤ n ≤ 10^5), which are the total number of lights and the length of subsegment of lights that are being checked, respectively.

Output

For each test case print the answer, modulo 10^9+7. 

Formally, let M = 10^9+7. It can be shown that the answer can be expressed as an irreducible fraction p/q, where p and q are integers and q not ≡ 0 \pmod{M}. Output the integer equal to p ⋅ q^{-1} mod M. In other words, output such an integer x that 0 ≤ x < M and x ⋅ q ≡ p \pmod{M}.

Example

Input


3
3 2
15 2
40 15


Output


333333338
141946947
329622137

Note

Explanation of the first sample test case:

Let's write out all possible sequences of light toggles, which will make the device complete its operation:

  1. (1, 2) — 2 lights are turned on 
  2. (1, 3, 2) — 3 lights are turned on 
  3. (2, 1) — 2 lights are turned on 
  4. (2, 3) — 2 lights are turned on 
  5. (3, 2) — 2 lights are turned on 
  6. (3, 1, 2) — 3 lights are turned on 



Then the final expected value will be equal to 2/6 + 3/6 + 2/6 + 2/6 + 2/6 + 3/6 = 14/6 = 7/3. 

Then the required output will be 333333338, since 333333338 ⋅ 3 ≡ 7 \pmod{10^9+7}.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;

const int MOD = (int)1e9 + 7;
inline int add(int u, int v, int mod = MOD) {return (u += v) >= mod ? u - mod : u;}
inline int sub(int u, int v, int mod = MOD) {return (u -= v) < 0 ? u + mod : u;}
inline int mul(int u, int v, int mod = MOD) {return (long long)u * v % mod;}
inline int power(int u, int v, int mod = MOD) {int res = 1;for (; v; v >>= 1, u = mul(u, u, mod)) if (v & 1) res = mul(res, u, mod); return res;}
inline int inv(int u, int mod = MOD) {return power(u, mod - 2, mod);}
inline void add_to(int &u, int v, int mod = MOD) {u = add(u, v, mod);}
inline void sub_to(int &u, int v, int mod = MOD) {u = sub(u, v, mod);}
inline void mul_to(int &u, int v, int mod = MOD) {u = mul(u, v, mod);}

const int N = 200010;

int fac[N];
int inv_fac[N];

int main() {
  ios_base::sync_with_stdio(0); cin.tie(0);
  fac[0] = 1;
  for (int i = 1; i < N; i++) {
    fac[i] = mul(fac[i - 1], i);
  }
  inv_fac[N - 1] = inv(fac[N - 1]);
  for (int i = N - 2; i >= 0; i--) {
    inv_fac[i] = mul(inv_fac[i + 1], i + 1);
  }

  auto nAk = [&](int n, int k) {
    if (k < 0 || k > n) return 0;
    return mul(fac[n], inv_fac[n - k]);
  };

  int tc;
  cin >> tc;
  while (tc--) {
    int n, k;
    cin >> n >> k;
    vector<int> dp(n + 2, 0);
    for (int i = 1; i <= n && n >= (k - 1) * (i - 1); i++) {
      dp[i] = nAk(n - (k - 1) * (i - 1), i);
    }
    int res = 0;
    int cur_prob = 1;
    for (int i = 1; i < n; i++) {
      int cur = mul(dp[i], n - i);
      int nxt = dp[i + 1];
      int now = sub(cur, nxt);
      add_to(res, mul(i + 1, mul(cur_prob, mul(now, inv(cur)))));
      mul_to(cur_prob, mul(nxt, inv(cur)));
    }
    // cout << mul(sum_w, inv(sum)) << '\n';
    cout << res << '\n';
  }
  return 0;
}