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;
using ll=long long;
const ll MOD=1e9+7;
const int INF=1e9;
const ll LINF=(ll)1e18;

struct Combination{
    vector<ll> fac,finv,inv;
    Combination(int mx){init(mx);}
    void init(int mx){
        fac.resize(mx+1);
        finv.resize(mx+1);
        inv.resize(mx+1);
        fac[0]=fac[1]=1;
        finv[0]=finv[1]=1;
        inv[1]=1;
        for(int i=2;i<=mx;i++){
            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 calc(int n,int k){
        return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD;
    }
};

int main(){
    Combination comb(2000010);
    int r1,r2,c1,c2;
    cin>>r1>>c1>>r2>>c2;
    ll ans=comb.calc(r2+c2+2,r2+1)-comb.calc(r1-1+c2+2,r1-1+1)-comb.calc(r2+c1-1+2,r2+1)+comb.calc(r1-1+c1-1+2,r1-1+1);
    cout<<(ans+MOD)%MOD<<endl;
}
