Snuke is standing on a two-dimensional plane. In one operation, he can move by 1 in the positive x-direction, or move by 1 in the positive y-direction.

Let us define a function f(r, c) as follows:

* f(r,c) :=  (The number of paths from the point (0, 0) to the point (r, c) that Snuke can trace by repeating the operation above)



Given are integers r_1, r_2, c_1, and c_2. Find the sum of f(i, j) over all pair of integers (i, j) such that r_1 ≤ i ≤ r_2 and c_1 ≤ j ≤ c_2, and compute this value modulo (10^9+7).

Constraints

* 1 ≤ r_1 ≤ r_2 ≤ 10^6
* 1 ≤ c_1 ≤ c_2 ≤ 10^6
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


r_1 c_1 r_2 c_2


Output

Print the sum of f(i, j) modulo (10^9+7).

Examples

Input

1 1 2 2


Output

14


Input

314 159 2653 589


Output

602215194
#include <stdio.h>
#define mod 1000000007
typedef long long ll;
 
ll rev(ll a) {
  ll b = mod - 2, ans = 1;
  while(b) {
    if(b & 1) ans *= a, ans %= mod;
    b >>= 1, a *= a, a %= mod;
  }
  return ans;
}
 
int main(void) {
  ll i, j, k, r[2], c[2], ans = 0, now;
  scanf("%lld%lld%lld%lld", &r[0], &c[0], &r[1], &c[1]);
  r[0]--, c[0]--;
  ll n = r[1] + c[1], fact[n + 10];
  fact[0] = 1;
  for(i = 1; i <= n + 9; ++i) fact[i] = fact[i - 1] * i, fact[i] %= mod;
  for(i = 0; i < 2; ++i) for(j = 0; j < 2; ++j) {
    now = fact[c[i] + r[j] + 2] * rev(fact[c[i] + 1]);
    now %= mod;
    now *= rev(fact[r[j] + 1]);
    now %= mod;
    ans += now * ((i ^ j) ? -1 : 1) + mod;
    ans %= mod;
  }
  printf("%lld", ans);
  return 0;
}