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;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n)   FOR(i,0,n)
#define pb emplace_back
typedef long long ll;
typedef pair<int,int> pint;


const int MAX_N=2000005;
const ll mod=1000000007;
ll fact[MAX_N+1];
ll inv[MAX_N+1],finv[MAX_N+1];
int inv_init(ll n,ll p){
    inv[1]=1;
    FOR(i,2,n+1) inv[i]=p-(p/i)*inv[p%i]%p;
    fact[0]=finv[0]=1;
    FOR(i,1,n+1){
        fact[i]=fact[i-1]*i%p;
        finv[i]=finv[i-1]*inv[i]%p;
    }
    return 0;
}
ll comb_mod(ll n,ll k,ll p){
    if(k<0||n<k) return 0;
    return finv[k]*finv[n-k]%p*fact[n]%p;
}
int r1,c1,r2,c2;
int main(){
    cin>>r1>>c1>>r2>>c2;
    inv_init(2000004,mod);
    cout<<(comb_mod(r2+c2+2,c2+1,mod)-comb_mod(r2+c1+1,c1,mod)-comb_mod(r1+c2+1,r1,mod)+comb_mod(r1+c1,c1,mod)+mod*10)%mod<<endl;
    return 0;
}