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;
const ll mod=1000000007;

ll qpow(ll a,ll n){
    ll res=1;
    while(n){
        if(n&1){
            res=res*a%mod;
        }
        a=a*a%mod;
        n>>=1;
    }
    return res;
}

ll fac[2000005],inv[2000005];

inline ll f(ll r,ll c){
    return ((ll)fac[r+c]*inv[r]%mod*inv[c]%mod);
}

inline ll g(ll r,ll c){
    ll res=0;
    for(ll i=1;i<=r+1;i++){
        res+=f(i,c);
    }
    return (res%mod);
}

int main(){

    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    fac[0]=1;
    inv[0]=1;
    for(ll i=1;i<=2000002;i++){
        fac[i]=(ll)fac[i-1]*i%mod;
        inv[i]=qpow(fac[i],mod-2);
    }
    ll r1,c1,r2,c2;
    cin>>r1>>c1>>r2>>c2;
    cout<<((g(r2,c2)-g(r2,c1-1)-g(r1-1,c2)+g(r1-1,c1-1))%mod+mod)%mod<<endl;

    return 0;
}