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 = 1000000007;
int inv[2000010];
void inel()
{
    inv[1] = 1;
    for(int i = 2;i <= 2000008;i++)
    {
        inv[i] = 1ll * (mod-mod/i) * inv[mod % i] % mod;
    }
}
int C(int n, int k)
{
	ll ans = 1;
	for (int i = 1;i <= n;++i)
	{
		ans = ans * i % mod;
	}
	for (int i = 1;i <= k;++i)
	{
		ans = ans * inv[i] % mod;
	}
	for (int i = 1;i <= n-k;++i)
	{
		ans = ans * inv[i] % mod;
	}
	return ans;
}
int main()
{
 	ios::sync_with_stdio(0);
 	inel();
 	int r1, c1, r2, c2;
 	cin >> r1 >> c1 >> r2 >> c2;
	ll ans = 0;
	ans = (ll)C(c2+r2+2,c2+1) + (ll)C(c1+r1,c1) + (ll)mod + (ll)mod - (ll)C(c2+r1+1,c2+1) - (ll)C(c1+r2+1,c1);
	ans %= mod;
	cout << ans << endl;
	return 0;
}

