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
//
// Created by munaiyi on 2020/3/18.
//

#include <bits/stdc++.h>

using namespace std;

const int maxn = 2e6 + 5;
const int mod = 1e9 + 7;

long long fac[maxn], inv[maxn];

void init() {
    inv[1] = inv[0] = 1;
    fac[1] = 1;
    for (int i = 2; i < maxn; i++) {
        fac[i] = fac[i - 1] * i % mod;
        inv[i] = (mod - mod / i) * inv[mod % i] % mod;
    }
    for (int i = 2; i < maxn; i++) {
        inv[i] = inv[i - 1] * inv[i] % mod;
    }
}

long long C(int a, int b) {
    if (a <= 0 || b < 0 || b > a) return 0;
    return fac[a] * inv[b] % mod * inv[a - b] % mod;
}

int main() {
    init();
    int x1, x2, y1, y2;
    scanf("%d%d%d%d", &x1, &y1, &x2, &y2);
    long long ans = 0;
    for (int i = x1; i <= x2; i++) {
        ans += C(i + y2 + 1, y2) - C(i + y1, y1 - 1);
    }
    ans = (ans % mod + mod) % mod;
    printf("%lld\n", ans);
    return 0;
}