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;
#define num 1000000007
//#define num 998244353
#define REP(i,a,n) for(ll i=a;i<n;i++)
#define inarr(i,a,n,A) for(ll i=a;i<n;i++) { cin>>A[i]; }
#define vll vector<long long>
#define pii pair <int,int>
#define pll pair<long long, long long>
#define vpii vector< pair <int,int>>
#define vpll vector< pair<long long, long long>>
#define max(a,b) ((a>b)?a:b)
#define min(a,b) ((a>b)?b:a)
#define max3(a,b,c) ((a>b)?(a>c)?a:c:(b>c)?b:c)
#define min3(a,b,c) ((a<b)?(a<c)?a:c:(b<c)?b:c)
#define avg(a,b) ((a)+(b))/2
#define push push_back
#define pop pop_back
#define sf int flag=0     //Remember semicolon
#define assmin(a,b) if(b<=a) { a=b; }
#define assmax(a,b) if(b>=a) { a=b; }
#define f first
#define s second
#define fix(f,n) std::fixed<<std::setprecision(n)<<f
typedef long long ll;
ll mod(ll a, ll b)
{
	if(a%b<0)
	{
		return a%b + b;
	}
	return a%b;
}
 
 
ll mod_exp(ll a, ll b, ll c)
{
	ll res=1;
	a=a%c;
	while(b>0)
	{
		if(b%2==1)
		{
			res=(res*a)%c;
		}
		b/=2;
		a=(a*a)%c;
	}
	return res;
}
ll mymod(ll a,ll b)
{
    return ((a%b)+b)%b;
}
bool prime[200001];
void SieveOfEratosthenes() 
{ 
    memset(prime, true, sizeof(prime)); 
    prime[1]=false;
    for (int p=2; p*p<=200000; p++) 
    { 
        if (prime[p] == true) 
        { 
            for (int i=p*p; i<=200000; i += p) 
                prime[i] = false; 
        } 
    } 
    return;
}
ll powe[60];
void power()
{
    powe[0]=1;
    REP(i,1,15)
    {
        powe[i]=2*powe[i-1];
    }
}
ll gcdExtended(ll,ll,ll *,ll *);
ll modInverse(ll a, ll m) 
{ 
    ll x, y; 
    ll g = gcdExtended(a, m, &x, &y); 
        ll res = (x%m + m) % m;
        return res;
} 
ll gcdExtended(ll a, ll b, ll *x, ll *y) 
{ 
    if (a == 0) 
    { 
        *x = 0, *y = 1; 
        return b; 
    } 
    ll x1, y1; 
    ll gcd = gcdExtended(b%a, a, &x1, &y1); 
    *x = y1 - (b/a) * x1; 
    *y = x1; 
    return gcd; 
} 
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    ll r1,c1,r2,c2;
	cin>>r1>>c1>>r2>>c2;
	ll a=1,b=1,c=1,d=1;
	REP(i,1,r1+1)
	{
		a=mymod(a*i,num);
	}
	REP(i,1,c1+1)
	{
		b=mymod(b*i,num);
	}
	REP(i,1,r2+2)
	{
		c=mymod(c*i,num);
	}
	REP(i,1,c2+2)
	{
		d=mymod(d*i,num);
	}
	ll e=1,f=1,g=1,h=1;
	REP(i,1,r2+c2+3)
	{
		e=mymod(e*i,num);
	}
	REP(i,1,r1+c1+1)
	{
		f=mymod(f*i,num);
	}
	REP(i,1,r1+c2+2)
	{
		g=mymod(g*i,num);
	}
	REP(i,1,r2+c1+2)
	{
		h=mymod(h*i,num);
	}
	ll ans=0;
	ll temp=modInverse(mymod(c*d,num),num);
	ans+=mymod(e*temp,num);
	temp=modInverse(mymod(a*b,num),num);
	ans+=mymod(f*temp,num);
	temp=modInverse(mymod(a*d,num),num);
	ans-=mymod(g*temp,num);
	temp=modInverse(mymod(b*c,num),num);
	ans-=mymod(h*temp,num);
	cout<<mymod(ans,num);
	return 0;
}