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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
	static void Main(){
		Sc sc=new Sc();
		var s=sc.Ia;
		int m=s[2]+s[3]+10;
		Cb r=new Cb(m);
		Mint ans=0;
		for(int i = s[0];i<=s[2];i++) {
			ans+=r.C1(s[3]+1+i+1-2+1,i+1-1+1);
			ans-=r.C1(s[1]-1+1+i+1-2+1,i+1-1+1);
		}
		Console.WriteLine("{0}",ans);
	}
}
public struct Mint{
	const int mod=(int)1e9+7;
	private long d;
	public Mint(long d){this.d=d;}
	public static implicit operator Mint(long d){return new Mint(d%mod);}
	public static explicit operator long(Mint d){return d.d;}
	public override string ToString(){return d.ToString();}
	public static Mint operator+(Mint a,long b){a.d=(a.d+b)%mod;return a;}
	public static Mint operator+(Mint a,Mint b){a.d=(a.d+b.d)%mod;return a;}
	public static Mint operator-(Mint a,long b){a.d=(mod+a.d-b)%mod;return a;}
	public static Mint operator-(Mint a,Mint b){a.d=(mod+a.d-b.d)%mod;return a;}
	public static Mint operator*(Mint a,long b){a.d=(a.d*b)%mod;return a;}
	public static Mint operator*(Mint a,Mint b){a.d=(a.d*b.d)%mod;return a;}
	public static Mint operator/(Mint a,long b){a.d=(a.d*Mi(b))%mod;return a;}
	public static Mint operator/(Mint a,Mint b){a.d=(a.d*Mi(b.d))%mod;return a;}
	private static long Mi(long a){
		a=(a+mod)%mod;
		long b=mod,u=1,v=0;
		while(b>0){
			long t=a/b;
			a-=t*b;a^=b;b^=a;a^=b;
			u-=t*v;u^=v;v^=u;u^=v;
		}
		u%=mod;
		if(u<0){u+=mod;}
		return u%mod;
	}
}
public class Cb{
	private const int mod=(int)1e9+7;
	public long[] r;
	public Cb(int n){
		r=new long[n];
		r[0]=1;
		for(int i=1;i<n;i++){r[i]=(r[i-1]*i)%mod;}
	}
	public long C1(long n,long k){return (r[n]*Mi(r[k]*r[n-k]))%mod;}
	public long C2(long n,long k){
		long l=1;
		n%=mod;
		for(int i=1;i<=k;i++){l=(l*(n-i+1))%mod;l=(l*Mi(i))%mod;}
		return l;
	}
	public long P1(long n,long k){return n<k?0:(r[n]*Mi(r[n-k]))%mod;}
	public long Mi(long a){
		a=(a+mod)%mod;
		long b=mod,u=1,v=0;
		while(b>0){long t=a/b;a-=t*b;a^=b;b^=a;a^=b;u-=t*v;u^=v;v^=u;u^=v;}
		u%=mod;
		if(u<0){u+=mod;}
		return u%mod;
	}
}
public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public double[] Da2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),double.Parse);}}
	public double[] Da3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),double.Parse);}
	public double[] Da3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),double.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}