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 int mod = 1e9+7;
const int maxn = 2e6+10;

ll fac[maxn];
ll inv[maxn];

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

ll C(ll n, ll m) {
    return fac[n]*inv[m]%mod*inv[n-m]%mod;
}

ll solve(ll r, ll c) {
    return (C(r+c+2, r+1)-1+mod)%mod;
}

int main() {
    int r1, c1, r2, c2;
    scanf("%d%d%d%d", &r1, &c1, &r2, &c2);
    fac[0] = inv[0] = 1;
    for(int i=1; i<=r2+c2+5; i++) {
        fac[i] = fac[i-1]*i%mod;
        inv[i] = qpow(fac[i], mod-2);
    }
    ll ans = solve(r2, c2)-solve(r1-1, c2)-solve(r2, c1-1)+solve(r1-1, c1-1);
    ans = ((ans%mod)+mod)%mod;
    printf("%lld\n", ans);
    return 0;
}
