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 ll long long
#define MAX 4000005
#define P ((ll)1e9+7)
using namespace std;

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

ll fac[MAX], inv[MAX];

void init(){
    fac[0] = 1;
    for(int i = 1; i < MAX; i++){
        fac[i] = fac[i-1]*i%P;
    }
    inv[MAX-1] = qpow(fac[MAX-1], P-2);
    for(int i = MAX-2; i >= 0; i--){
        inv[i] = inv[i+1]*(i+1)%P;
    }
}

ll C(ll n, ll m){
    if(!m) return 1;
    return fac[n]*inv[m]%P*inv[n-m]%P;
}

ll calc(ll x, ll l, ll r){
    return (C(r+1, x+1)-C(l, x+1)+P)%P;
}

int main()
{
    init();
    ll x1, y1, x2, y2, ans = 0;
    cin >> x1 >> y1 >> x2 >> y2;
    for(int i = x1; i <= x2; i++){
        ans = (ans+calc(i, i+y1, i+y2))%P;
    }
    cout << ans << endl;

    return 0;
}
