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 Go (1.6) (judge verdict: Time Limit Exceeded)

package main

import "fmt"

const MOD = 1000000007

var fac [2000020]int

func bipow(n, m int) int {
	if m == 0 {
		return 1
	}
	if m%2 == 0 {
		return bipow((n*n)%MOD, m/2)
	} else {
		return (n * bipow(n, m-1)) % MOD
	}
}

func fill_table() {
	fac[0] = 1
	for i := 1; i < 2000020; i++ {
		fac[i] = (fac[i-1] * i) % MOD
	}
}

func comb(n, m int) int {
	a := fac[n]
	b := bipow(fac[m], MOD-2)
	c := bipow(fac[n-m], MOD-2)
	ret := (((a * b) % MOD) * c) % MOD
	return ret
}

func S(r, c int) int {
	ret := 0
	for j := 0; j <= c; j++ {
		ret += comb(j+r+1, r)
		ret %= MOD
	}
	return ret
}

func main() {
	var r1, c1, r2, c2 int
	fmt.Scan(&r1, &c1, &r2, &c2)

	fill_table()

	a := (S(r2, c2) + S(r1-1, c1-1)) % MOD
	b := (S(r2, c1-1) + S(r1-1, c2)) % MOD
	ans := (a + MOD - b) % MOD
	fmt.Println(ans)
}