Greg has a pad. The pad's screen is an n × m rectangle, each cell can be either black or white. We'll consider the pad rows to be numbered with integers from 1 to n from top to bottom. Similarly, the pad's columns are numbered with integers from 1 to m from left to right.

Greg thinks that the pad's screen displays a cave if the following conditions hold:

  * There is a segment [l, r] (1 ≤ l ≤ r ≤ n), such that each of the rows l, l + 1, ..., r has exactly two black cells and all other rows have only white cells. 
  * There is a row number t (l ≤ t ≤ r), such that for all pairs of rows with numbers i and j (l ≤ i ≤ j ≤ t) the set of columns between the black cells in row i (with the columns where is these black cells) is the subset of the set of columns between the black cells in row j (with the columns where is these black cells). Similarly, for all pairs of rows with numbers i and j (t ≤ i ≤ j ≤ r) the set of columns between the black cells in row j (with the columns where is these black cells) is the subset of the set of columns between the black cells in row i (with the columns where is these black cells). 



Greg wondered, how many ways there are to paint a cave on his pad. Two ways can be considered distinct if there is a cell that has distinct colors on the two pictures.

Help Greg.

Input

The first line contains two integers n, m — the pad's screen size (1 ≤ n, m ≤ 2000).

Output

In the single line print the remainder after dividing the answer to the problem by 1000000007 (109 + 7).

Examples

Input

1 1


Output

0


Input

4 4


Output

485


Input

3 5


Output

451
#include <bits/stdc++.h>
using namespace std;
struct FFT {
  struct node {
    double x, y;
    node() {}
    node(double a, double b) : x(a), y(b) {}
    node operator+(const node &a) const {
      return node(this->x + a.x, this->y + a.y);
    }
    node operator-(const node a) const {
      return node(this->x - a.x, this->y - a.y);
    }
    node operator*(const node a) const {
      return node(this->x * a.x - this->y * a.y, this->x * a.y + a.x * this->y);
    }
  };
  long long M;
  vector<node> A, B, w[2];
  vector<long long> rev;
  long double pi = acos(-1.0);
  void init(long long n) {
    M = 1;
    while (M < n) M <<= 1;
    M <<= 1;
    A.resize(M);
    B.resize(M);
    w[0].resize(M);
    w[1].resize(M);
    rev.resize(M);
    for (long long i = 0; i < M; i++) {
      long long j = i, y = 0;
      for (long long x = 1; x < M; x <<= 1, j >>= 1) (y <<= 1) += j & 1;
      rev[i] = y;
    }
    for (long long i = 0; i < M; i++) {
      w[0][i] = node(cos(2 * pi * i / M), sin(2 * pi * i / M));
      w[1][i] = node(cos(2 * pi * i / M), -sin(2 * pi * i / M));
    }
  }
  void ftransform(vector<node> &A, long long p) {
    for (long long i = 0; i < M; i++)
      if (i < rev[i]) swap(A[i], A[rev[i]]);
    for (long long i = 1; i < M; i <<= 1)
      for (long long j = 0, t = M / (i << 1); j < M; j += i << 1)
        for (long long k = 0, l = 0; k < i; k++, l += t) {
          node x = w[p][l] * A[i + j + k];
          node y = A[j + k];
          A[j + k] = y + x;
          A[j + k + i] = y - x;
        }
    if (p)
      for (long long i = 0; i < M; i++) A[i].x /= M;
  }
  void multiply(vector<long long> &P, vector<long long> &Q,
                vector<long long> &res) {
    init(max(P.size(), Q.size()));
    for (long long i = 0; i < M; i++) A[i].x = A[i].y = B[i].x = B[i].y = 0;
    for (long long i = 0; i < P.size(); i++) A[i].x = P[i];
    for (long long i = 0; i < Q.size(); i++) B[i].x = Q[i];
    ftransform(A, 0);
    ftransform(B, 0);
    for (long long k = 0; k < M; k++) A[k] = A[k] * B[k];
    ftransform(A, 1);
    res.resize(M);
    for (long long i = 0; i < M; i++) res[i] = round(A[i].x);
  }
} fft;
namespace FFT_tourist {
struct num {
  double x, y;
  num() { x = y = 0; }
  num(double x, double y) : x(x), y(y) {}
};
inline num operator+(num a, num b) { return num(a.x + b.x, a.y + b.y); }
inline num operator-(num a, num b) { return num(a.x - b.x, a.y - b.y); }
inline num operator*(num a, num b) {
  return num(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x);
}
inline num conj(num a) { return num(a.x, -a.y); }
int base = 1;
vector<num> roots = {{0, 0}, {1, 0}};
vector<int> rev = {0, 1};
const double PI = acosl(-1.0);
void ensure_base(int nbase) {
  if (nbase <= base) return;
  rev.resize(1 << nbase);
  for (int i = 0; i < (1 << nbase); i++)
    rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
  roots.resize(1 << nbase);
  while (base < nbase) {
    double angle = 2 * PI / (1 << (base + 1));
    for (int i = 1 << (base - 1); i < (1 << base); i++) {
      roots[i << 1] = roots[i];
      double angle_i = angle * (2 * i + 1 - (1 << base));
      roots[(i << 1) + 1] = num(cos(angle_i), sin(angle_i));
    }
    base++;
  }
}
void fft(vector<num> &a, int n = -1) {
  if (n == -1) n = a.size();
  assert((n & (n - 1)) == 0);
  int zeros = __builtin_ctz(n);
  ensure_base(zeros);
  int shift = base - zeros;
  for (int i = 0; i < n; i++)
    if (i < (rev[i] >> shift)) swap(a[i], a[rev[i] >> shift]);
  for (int k = 1; k < n; k <<= 1) {
    for (int i = 0; i < n; i += 2 * k) {
      for (int j = 0; j < k; j++) {
        num z = a[i + j + k] * roots[j + k];
        a[i + j + k] = a[i + j] - z;
        a[i + j] = a[i + j] + z;
      }
    }
  }
}
vector<num> fa, fb;
vector<int> multiply(vector<int> &a, vector<int> &b) {
  int need = a.size() + b.size() - 1;
  int nbase = 0;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  if (sz > (int)fa.size()) fa.resize(sz);
  for (int i = 0; i < sz; i++) {
    int x = (i < (int)a.size() ? a[i] : 0);
    int y = (i < (int)b.size() ? b[i] : 0);
    fa[i] = num(x, y);
  }
  fft(fa, sz);
  num r(0, -0.25 / sz);
  for (int i = 0; i <= (sz >> 1); i++) {
    int j = (sz - i) & (sz - 1);
    num z = (fa[j] * fa[j] - conj(fa[i] * fa[i])) * r;
    if (i != j) fa[j] = (fa[i] * fa[i] - conj(fa[j] * fa[j])) * r;
    fa[i] = z;
  }
  fft(fa, sz);
  vector<int> res(need);
  for (int i = 0; i < need; i++) res[i] = fa[i].x + 0.5;
  return res;
}
vector<int> multiply_mod(vector<int> &a, vector<int> &b, int m, int eq = 0) {
  int need = a.size() + b.size() - 1;
  int nbase = 0;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  if (sz > (int)fa.size()) fa.resize(sz);
  for (int i = 0; i < (int)a.size(); i++) {
    int x = (a[i] % m + m) % m;
    fa[i] = num(x & ((1 << 15) - 1), x >> 15);
  }
  fill(fa.begin() + a.size(), fa.begin() + sz, num{0, 0});
  fft(fa, sz);
  if (sz > (int)fb.size()) fb.resize(sz);
  if (eq)
    copy(fa.begin(), fa.begin() + sz, fb.begin());
  else {
    for (int i = 0; i < (int)b.size(); i++) {
      int x = (b[i] % m + m) % m;
      fb[i] = num(x & ((1 << 15) - 1), x >> 15);
    }
    fill(fb.begin() + b.size(), fb.begin() + sz, num{0, 0});
    fft(fb, sz);
  }
  double ratio = 0.25 / sz;
  num r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
  for (int i = 0; i <= (sz >> 1); i++) {
    int j = (sz - i) & (sz - 1);
    num a1 = (fa[i] + conj(fa[j]));
    num a2 = (fa[i] - conj(fa[j])) * r2;
    num b1 = (fb[i] + conj(fb[j])) * r3;
    num b2 = (fb[i] - conj(fb[j])) * r4;
    if (i != j) {
      num c1 = (fa[j] + conj(fa[i]));
      num c2 = (fa[j] - conj(fa[i])) * r2;
      num d1 = (fb[j] + conj(fb[i])) * r3;
      num d2 = (fb[j] - conj(fb[i])) * r4;
      fa[i] = c1 * d1 + c2 * d2 * r5;
      fb[i] = c1 * d2 + c2 * d1;
    }
    fa[j] = a1 * b1 + a2 * b2 * r5;
    fb[j] = a1 * b2 + a2 * b1;
  }
  fft(fa, sz);
  fft(fb, sz);
  vector<int> res(need);
  for (int i = 0; i < need; i++) {
    long long aa = fa[i].x + 0.5;
    long long bb = fb[i].x + 0.5;
    long long cc = fa[i].y + 0.5;
    res[i] = (aa + ((bb % m) << 15) + ((cc % m) << 30)) % m;
  }
  return res;
}
vector<int> square_mod(vector<int> &a, int m) {
  return multiply_mod(a, a, m, 1);
}
};  // namespace FFT_tourist
long long dp[2005][2005];
long long pd[2005][2005];
const long long mod = 1e9 + 7;
int main() {
  long long n, m;
  cin >> n >> m;
  for (int width = 2; width <= m; width++) {
    dp[1][width] = 1;
    pd[1][width] = 1;
  }
  for (int len = 2; len <= n; len++) {
    vector<long long> mul(m, 0);
    for (int i = 0; i < m; i++) {
      mul[i] = i + 1;
    }
    vector<long long> f(m + 1, 0);
    for (int i = 1; i <= m; i++) f[i] = dp[len - 1][i];
    vector<long long> res;
    fft.multiply(mul, f, res);
    for (int i = 2; i <= m; i++)
      dp[len][i] = res[i], pd[len][i] = (dp[len][i] - dp[len - 1][i]) % mod;
  }
  long long ans = 0;
  for (int base = 2; base <= m; base++) {
    vector<int> up(n + 1, 0), down(n + 1, 0);
    for (int len = 1; len <= n; len++) {
      up[len] = pd[len][base];
      down[len] = dp[len][base];
    }
    vector<int> res;
    res = FFT_tourist::multiply_mod(up, down, mod);
    long long cur = 0;
    for (int len = 1; len <= n; len++) {
      long long x = (1ll * res[len + 1] * (n - len + 1)) % mod;
      cur += x;
      cur %= mod;
    }
    cur *= (m - base + 1);
    cur %= mod;
    ans += cur;
    ans %= mod;
  }
  cout << ans << "\n";
}
