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<bits/stdc++.h>
#define rep(i, n) for (int i=0; i<(n); i++)
#define ll long long
using namespace std;

const int MAX=2020202;
const int MOD=1000000007;

ll fac[MAX], finv[MAX], inv[MAX];

void COMinit() {
  fac[0]=fac[1]=1;
  finv[0]=finv[1]=1;
  inv[1]=1;
  rep(i, MAX) {
    if (i==0||i==1) continue;
    fac[i]=fac[i-1]*i%MOD;
    inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;
    finv[i]=finv[i-1]*inv[i]%MOD;
  }
}

ll COM(int n, int k) {
  if (n<k) return 0;
  if (n<0||k<0) return 0;
  return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD;
}

int main() {
  int r1,r2,c1,c2;
  cin>>r1>>c1>>r2>>c2;
  COMinit();
  ll res=0;
  rep(i, r2-r1+1) {
    res+=COM(r1+c2+1+i, r1+1+i);
    res-=COM(r1+c1+i, r1+1+i);
    if (res<0) res+=MOD;
    res%=MOD;
  }
  cout<<res<<endl;
}