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;

ll MOD = 1000000007;

vector<ll> fac;
vector<ll> ifac;

ll modinv(ll a) {
    ll b = MOD, u = 1, v = 0;
    while (b) {
        ll t = a / b;
        a -= t * b; swap(a, b);
        u -= t * v; swap(u, v);
    }
    u %= MOD;
    if (u < 0) u += MOD;
    return u;
}

ll f(ll r, ll c) {
    return (fac[r + c] * ifac[r] % MOD) * ifac[c] % MOD; }

ll g(ll r, ll c) { return f(r+1, c+1) - 1; }

int main() {
    ll r1, r2, c1, c2;
    cin >> r1 >> c1 >> r2 >> c2;
    ll t = 1;
    fac.push_back(t);
    ifac.push_back(1);
    for(auto i = 1; i < r2 + c2 + 3; i++) {
        t *= i;
        t %= MOD;
        fac.push_back(t);
        ifac.push_back(modinv(t));
    }
    ll ans =
        (g(r2, c2) - g(r2, c1 - 1) - g(r1 - 1, c2) + g(r1 - 1, c1 - 1) + MOD * 2) % MOD;
    cout << ans << endl;
    return 0;
}