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 <iostream>
#include <cstdio>

using namespace std;

typedef long long ll;

const ll M = 1e9 + 7;

ll r1, r2, c1, c2;
ll fac[2000005];
ll fiv[2000005];

ll C(ll p, ll q)
{
    return fac[p] * fiv[q] % M * fiv[p - q] % M;
}

int main()
{
    scanf("%lld%lld%lld%lld", &r1, &c1, &r2, &c2);
    r2++, c2++;
    fac[0] = 1;
    fiv[r2 + c2] = 1;
    for(ll i = 1; i <= r2 + c2; i++) fac[i] = fac[i - 1] * i % M;
    ll now = fac[r2 + c2];
    for(ll i = 0; (1 << i) <= (M - 2); i++)
    {
        if((1 << i) & (M - 2)) fiv[r2 + c2] *= now, fiv[r2 + c2] %= M;
        now *= now;
        now %= M;
    }
    for(ll i = r2 + c2 - 1; i >= 0; i--)
    {
        fiv[i] = fiv[i + 1] * (i + 1) % M;
    }
    ll ans = 0;
    ans += C(r2 + c2, r2);
    ans -= C(r2 + c1, r2);
    ans -= C(r1 + c2, r1);
    ans += C(r1 + c1, r1);
    ans += 2 * M;
    ans %= M;
    printf("%lld\n", ans);
    return 0;
}
