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>
using namespace std;
typedef long long ll;
typedef double dd;
const int N = 2e6+5;
const double eps = 1e-8;
const int mod = 1e9+7;

inline ll qpow(long long a, int b) {
  ll ans = 1;
  a = (a % mod + mod) % mod;
  for (; b; b >>= 1) {
    if (b & 1) ans = (a * ans) % mod;
    a = (a * a) % mod;
  }
  return ans;
}

ll r1,r2,c1,c2,fac[N];

ll com(ll m,ll n){
  ll ans = fac[m];
  ans = (ans*qpow(fac[n],mod-2))%mod;
  ans = (ans*qpow(fac[m-n],mod-2))%mod;
  return ans%mod;
}

int main(){
  // freopen("input.txt","r",stdin);
  cin>>r1>>c1>>r2>>c2;
  fac[0] = 1;
  for(int i = 1;i <= 2e6+3;i++) fac[i] = ((fac[i-1]%mod)*(i%mod))%mod;
  ll x= com(r2+c2+2,c2+1);
  ll y = com(r1+c2+1,c2+1);
  ll z = com(r2+c1+1,c1);
  ll w = com(r1+c1,c1);
  ll ans = (x-y+mod)%mod;
  ans = (ans + w%mod)%mod;
  ans = (ans-z+mod)%mod;
  cout << ans << endl;  
  return 0;
}
