#include <bits/stdc++.h>
using namespace std;
template <class T>
using rque = priority_queue<T, vector<T>, greater<T>>;
const long long mod = (int)1e9 + 7;
template <class T>
bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmax(T &a, const T &b) {
  if (b > a) {
    a = b;
    return 1;
  }
  return 0;
}
long long gcd(long long a, long long b) {
  if (a == 0) return b;
  if (b == 0) return a;
  long long c = a % b;
  while (c != 0) {
    a = b;
    b = c;
    c = a % b;
  }
  return b;
}
long long extGCD(long long a, long long b, long long &x, long long &y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  }
  long long d = extGCD(b, a % b, y, x);
  y -= a / b * x;
  return d;
}
struct UnionFind {
  vector<long long> data;
  int num;
  UnionFind(int sz) {
    data.assign(sz, -1);
    num = sz;
  }
  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y) return (false);
    if (data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    num--;
    return (true);
  }
  int find(int k) {
    if (data[k] < 0) return (k);
    return (data[k] = find(data[k]));
  }
  long long size(int k) { return (-data[find(k)]); }
};
long long M = 1000000007;
template <int mod>
struct ModInt {
  int x;
  ModInt() : x(0) {}
  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }
  ModInt operator-() const { return ModInt(-x); }
  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
  bool operator==(const ModInt &p) const { return x == p.x; }
  bool operator!=(const ModInt &p) const { return x != p.x; }
  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }
  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }
  static int get_mod() { return mod; }
};
using mint = ModInt<mod>;
mint mpow(mint x, long long n) {
  mint ans = 1;
  while (n != 0) {
    if (n & 1) ans *= x;
    x *= x;
    n = n >> 1;
  }
  return ans;
}
long long mpow2(long long x, long long n, long long mod) {
  long long ans = 1;
  while (n != 0) {
    if (n & 1) ans = ans * x % mod;
    x = x * x % mod;
    n = n >> 1;
  }
  return ans;
}
vector<mint> fac;
vector<mint> ifac;
void setcomb(int sz = 2000010) {
  fac.assign(sz + 1, 0);
  ifac.assign(sz + 1, 0);
  fac[0] = 1;
  for (long long i = 0; i < sz; i++) {
    fac[i + 1] = fac[i] * (i + 1);
  }
  ifac[sz] = fac[sz].inverse();
  for (long long i = sz; i > 0; i--) {
    ifac[i - 1] = ifac[i] * i;
  }
}
mint comb(long long a, long long b) {
  if (fac.size() == 0) setcomb();
  if (a == 0 && b == 0) return 1;
  if (a < b || a < 0) return 0;
  return ifac[a - b] * ifac[b] * fac[a];
}
mint perm(long long a, long long b) {
  if (fac.size() == 0) setcomb();
  if (a == 0 && b == 0) return 1;
  if (a < b || a < 0) return 0;
  return fac[a] * ifac[a - b];
}
long long modinv(long long a) {
  long long b = M, u = 1, v = 0;
  while (b) {
    long long t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= M;
  if (u < 0) u += M;
  return u;
}
long long modinv2(long long a, long long mod) {
  long long b = mod, u = 1, v = 0;
  while (b) {
    long long t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= mod;
  if (u < 0) u += mod;
  return u;
}
template <class T>
struct Matrix {
  vector<vector<T>> A;
  Matrix() {}
  Matrix(size_t n, size_t m) : A(n, vector<T>(m, 0)) {}
  Matrix(size_t n) : A(n, vector<T>(n, 0)){};
  size_t height() const { return (A.size()); }
  size_t width() const { return (A[0].size()); }
  inline const vector<T> &operator[](int k) const { return (A.at(k)); }
  inline vector<T> &operator[](int k) { return (A.at(k)); }
  static Matrix I(size_t n) {
    Matrix mat(n);
    for (int i = 0; i < n; i++) mat[i][i] = 1;
    return (mat);
  }
  Matrix &operator+=(const Matrix &B) {
    size_t n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j];
    return (*this);
  }
  Matrix &operator-=(const Matrix &B) {
    size_t n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j];
    return (*this);
  }
  Matrix &operator*=(const Matrix &B) {
    size_t n = height(), m = B.width(), p = width();
    assert(p == B.height());
    vector<vector<T>> C(n, vector<T>(m, 0));
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++)
        for (int k = 0; k < p; k++)
          C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
    A.swap(C);
    return (*this);
  }
  Matrix &operator^=(long long k) {
    Matrix B = Matrix::I(height());
    while (k > 0) {
      if (k & 1) B *= *this;
      *this *= *this;
      k >>= 1LL;
    }
    A.swap(B.A);
    return (*this);
  }
  Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }
  Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }
  Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }
  Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }
  friend ostream &operator<<(ostream &os, Matrix &p) {
    size_t n = p.height(), m = p.width();
    for (int i = 0; i < n; i++) {
      os << "[";
      for (int j = 0; j < m; j++) {
        os << p[i][j] << (j + 1 == m ? "]\n" : ",");
      }
    }
    return (os);
  }
  T determinant() {
    Matrix B(*this);
    assert(width() == height());
    T ret = 1;
    for (int i = 0; i < width(); i++) {
      int idx = -1;
      for (int j = i; j < width(); j++) {
        if (B[j][i] != 0) idx = j;
      }
      if (idx == -1) return (0);
      if (i != idx) {
        ret *= -1;
        swap(B[i], B[idx]);
      }
      ret *= B[i][i];
      T vv = B[i][i];
      for (int j = 0; j < width(); j++) {
        B[i][j] /= vv;
      }
      for (int j = i + 1; j < width(); j++) {
        T a = B[j][i];
        for (int k = 0; k < width(); k++) {
          B[j][k] -= B[i][k] * a;
        }
      }
    }
    return (ret);
  }
};
int main() {
  ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  mint dp[1001][1001] = {};
  dp[0][0] = 1;
  for (long long i = 0; i < (1000); i++) {
    for (long long j = 0; j < (1001); j++) {
      for (long long nj = j + i + 1; nj <= 1000; nj += i + 1)
        dp[i + 1][nj] += dp[i][j];
    }
  }
  setcomb();
  int T;
  cin >> T;
  while (T--) {
    long long n, k;
    cin >> n >> k;
    mint ans = 0;
    for (long long i = (k - 1) * k / 2; i < (n - k + 1); i++)
      ans += (dp[k][i] + dp[k - 1][i]) * comb(n - i, k);
    ans *= fac[k];
    cout << ans << endl;
  }
}

### Prompt

Generate a CPP solution to the following problem:

The sequence of integer pairs (a1, b1), (a2, b2), ..., (ak, bk) is beautiful, if the following statements are fulfilled: 

  * 1 ≤ a1 ≤ b1 < a2 ≤ b2 < ... < ak ≤ bk ≤ n, where n is a given positive integer; 
  * all numbers b1 - a1, b2 - a2, ..., bk - ak are distinct. 



For the given number n find the number of beautiful sequences of length k. As the answer can be rather large, print the remainder after dividing it by 1000000007 (109 + 7).

Input

The first line contains integer t (1 ≤ t ≤ 2·105) — the number of the test data.

Each of the next t lines contains two integers n and k (1 ≤ k ≤ n ≤ 1000).

Output

For each test from the input print the answer to the problem modulo 1000000007 (109 + 7). Print the answers to the tests in the order in which the tests are given in the input.

Examples

Input

6
1 1
2 1
2 2
3 1
3 2
3 3


Output

1
3
0
6
2
0

Note

In the first test sample there is exactly one beautiful sequence: (1, 1).

In the second test sample, the following sequences are beautiful: 

  * (1, 1); 
  * (1, 2); 
  * (2, 2). 



In the fourth test sample, the following sequences are beautiful: 

  * (1, 1); 
  * (1, 2); 
  * (1, 3); 
  * (2, 2); 
  * (2, 3); 
  * (3, 3). 



In the fifth test sample, the following sequences are beautiful: 

  * (1, 1), (2, 3); 
  * (1, 2), (3, 3). 



In the third and sixth samples, there are no beautiful sequences.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <class T>
using rque = priority_queue<T, vector<T>, greater<T>>;
const long long mod = (int)1e9 + 7;
template <class T>
bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmax(T &a, const T &b) {
  if (b > a) {
    a = b;
    return 1;
  }
  return 0;
}
long long gcd(long long a, long long b) {
  if (a == 0) return b;
  if (b == 0) return a;
  long long c = a % b;
  while (c != 0) {
    a = b;
    b = c;
    c = a % b;
  }
  return b;
}
long long extGCD(long long a, long long b, long long &x, long long &y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  }
  long long d = extGCD(b, a % b, y, x);
  y -= a / b * x;
  return d;
}
struct UnionFind {
  vector<long long> data;
  int num;
  UnionFind(int sz) {
    data.assign(sz, -1);
    num = sz;
  }
  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y) return (false);
    if (data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    num--;
    return (true);
  }
  int find(int k) {
    if (data[k] < 0) return (k);
    return (data[k] = find(data[k]));
  }
  long long size(int k) { return (-data[find(k)]); }
};
long long M = 1000000007;
template <int mod>
struct ModInt {
  int x;
  ModInt() : x(0) {}
  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }
  ModInt operator-() const { return ModInt(-x); }
  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
  bool operator==(const ModInt &p) const { return x == p.x; }
  bool operator!=(const ModInt &p) const { return x != p.x; }
  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }
  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }
  static int get_mod() { return mod; }
};
using mint = ModInt<mod>;
mint mpow(mint x, long long n) {
  mint ans = 1;
  while (n != 0) {
    if (n & 1) ans *= x;
    x *= x;
    n = n >> 1;
  }
  return ans;
}
long long mpow2(long long x, long long n, long long mod) {
  long long ans = 1;
  while (n != 0) {
    if (n & 1) ans = ans * x % mod;
    x = x * x % mod;
    n = n >> 1;
  }
  return ans;
}
vector<mint> fac;
vector<mint> ifac;
void setcomb(int sz = 2000010) {
  fac.assign(sz + 1, 0);
  ifac.assign(sz + 1, 0);
  fac[0] = 1;
  for (long long i = 0; i < sz; i++) {
    fac[i + 1] = fac[i] * (i + 1);
  }
  ifac[sz] = fac[sz].inverse();
  for (long long i = sz; i > 0; i--) {
    ifac[i - 1] = ifac[i] * i;
  }
}
mint comb(long long a, long long b) {
  if (fac.size() == 0) setcomb();
  if (a == 0 && b == 0) return 1;
  if (a < b || a < 0) return 0;
  return ifac[a - b] * ifac[b] * fac[a];
}
mint perm(long long a, long long b) {
  if (fac.size() == 0) setcomb();
  if (a == 0 && b == 0) return 1;
  if (a < b || a < 0) return 0;
  return fac[a] * ifac[a - b];
}
long long modinv(long long a) {
  long long b = M, u = 1, v = 0;
  while (b) {
    long long t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= M;
  if (u < 0) u += M;
  return u;
}
long long modinv2(long long a, long long mod) {
  long long b = mod, u = 1, v = 0;
  while (b) {
    long long t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= mod;
  if (u < 0) u += mod;
  return u;
}
template <class T>
struct Matrix {
  vector<vector<T>> A;
  Matrix() {}
  Matrix(size_t n, size_t m) : A(n, vector<T>(m, 0)) {}
  Matrix(size_t n) : A(n, vector<T>(n, 0)){};
  size_t height() const { return (A.size()); }
  size_t width() const { return (A[0].size()); }
  inline const vector<T> &operator[](int k) const { return (A.at(k)); }
  inline vector<T> &operator[](int k) { return (A.at(k)); }
  static Matrix I(size_t n) {
    Matrix mat(n);
    for (int i = 0; i < n; i++) mat[i][i] = 1;
    return (mat);
  }
  Matrix &operator+=(const Matrix &B) {
    size_t n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j];
    return (*this);
  }
  Matrix &operator-=(const Matrix &B) {
    size_t n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j];
    return (*this);
  }
  Matrix &operator*=(const Matrix &B) {
    size_t n = height(), m = B.width(), p = width();
    assert(p == B.height());
    vector<vector<T>> C(n, vector<T>(m, 0));
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++)
        for (int k = 0; k < p; k++)
          C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
    A.swap(C);
    return (*this);
  }
  Matrix &operator^=(long long k) {
    Matrix B = Matrix::I(height());
    while (k > 0) {
      if (k & 1) B *= *this;
      *this *= *this;
      k >>= 1LL;
    }
    A.swap(B.A);
    return (*this);
  }
  Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }
  Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }
  Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }
  Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }
  friend ostream &operator<<(ostream &os, Matrix &p) {
    size_t n = p.height(), m = p.width();
    for (int i = 0; i < n; i++) {
      os << "[";
      for (int j = 0; j < m; j++) {
        os << p[i][j] << (j + 1 == m ? "]\n" : ",");
      }
    }
    return (os);
  }
  T determinant() {
    Matrix B(*this);
    assert(width() == height());
    T ret = 1;
    for (int i = 0; i < width(); i++) {
      int idx = -1;
      for (int j = i; j < width(); j++) {
        if (B[j][i] != 0) idx = j;
      }
      if (idx == -1) return (0);
      if (i != idx) {
        ret *= -1;
        swap(B[i], B[idx]);
      }
      ret *= B[i][i];
      T vv = B[i][i];
      for (int j = 0; j < width(); j++) {
        B[i][j] /= vv;
      }
      for (int j = i + 1; j < width(); j++) {
        T a = B[j][i];
        for (int k = 0; k < width(); k++) {
          B[j][k] -= B[i][k] * a;
        }
      }
    }
    return (ret);
  }
};
int main() {
  ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  mint dp[1001][1001] = {};
  dp[0][0] = 1;
  for (long long i = 0; i < (1000); i++) {
    for (long long j = 0; j < (1001); j++) {
      for (long long nj = j + i + 1; nj <= 1000; nj += i + 1)
        dp[i + 1][nj] += dp[i][j];
    }
  }
  setcomb();
  int T;
  cin >> T;
  while (T--) {
    long long n, k;
    cin >> n >> k;
    mint ans = 0;
    for (long long i = (k - 1) * k / 2; i < (n - k + 1); i++)
      ans += (dp[k][i] + dp[k - 1][i]) * comb(n - i, k);
    ans *= fac[k];
    cout << ans << endl;
  }
}

```