Problem:
Score : 600 points

Problem Statement

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).

Sample Input 1

1 1 2 2

Sample Output 1

14

For example, there are two paths from the point (0, 0) to the point (1, 1): (0,0) → (0,1) → (1,1) and (0,0) → (1,0) → (1,1), so f(1,1)=2.

Similarly, f(1,2)=3, f(2,1)=3, and f(2,2)=6. Thus, the sum is 14.

Sample Input 2

314 159 2653 589

Sample Output 2

602215194

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef int ll;
typedef long long int li;
const ll MAXN=2e6+51,MOD=1e9+7;
ll r1,r2,c1,c2,res;
ll fact[MAXN],finv[MAXN];
inline ll read()
{
    register ll num=0,neg=1;
    register char ch=getchar();
    while(!isdigit(ch)&&ch!='-')
    {
        ch=getchar();
    }
    if(ch=='-')
    {
        neg=-1;
        ch=getchar();
    }
    while(isdigit(ch))
    {
        num=(num<<3)+(num<<1)+(ch-'0');
        ch=getchar();
    }
    return num*neg;
} 
inline ll qpow(ll base,ll exponent)
{
    ll res=1;
    while(exponent)
    {
        if(exponent&1)
        {
            res=(li)res*base%MOD;
        }
        base=(li)base*base%MOD,exponent>>=1;
    }
    return res;
}
inline void setup(ll cnt)
{
	fact[0]=fact[1]=finv[0]=1;
	for(register int i=2;i<=cnt;i++)
	{
		fact[i]=(li)fact[i-1]*i%MOD;
	}
	finv[cnt]=qpow(fact[cnt],MOD-2);
	for(register int i=cnt-1;i;i--)
	{
		finv[i]=(li)finv[i+1]*(i+1)%MOD;
	}
}
int main()
{
	setup(2000010),r1=read(),c1=read(),r2=read(),c2=read();
	for(register int i=r1;i<=r2;i++)
	{
		res=(res+(li)fact[i+c2+1]*finv[i+1]%MOD*finv[c2]%MOD)%MOD;
		res=(res-((li)fact[i+c1]*finv[i+1]%MOD*finv[c1-1]%MOD)+MOD)%MOD;
	}
	printf("%d\n",res);
}