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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

import java.util.*

fun main(args: Array<String>) {
    val mod = 1000000007
    val (r0, c0, r1, c1) = readIntList()
        cmb = Comb(r1 + c1)
    var ans = 0L

    for (r in r0..r1) {
        for (c in c0..c1) {
            ans += (r + c C r)
            if (ans > Long.MAX_VALUE/2)
                ans %= mod
        }
    }
    println(ans % mod)
}

var cmb: Comb? = null

infix fun Int.C(k: Int) = cmb!![this, k]

class Comb(max: Int, val mod: Int = 1000000007) {
    val fac = LongArray(max + 1).apply { this[0] = 1L; this[1] = 1L }
    val finv = LongArray(max + 1).apply { this[0] = 1L; this[1] = 1L }
    val inv = LongArray(max + 1).apply { this[1] = 1L }

    init {
        for (i in 2..max) {
            fac[i] = fac[i - 1] * i % mod
            inv[i] = mod - inv[mod % i] * (mod / i) % mod
            finv[i] = finv[i - 1] * inv[i] % mod
        }
    }

    /**
     * nCk
     */
    operator fun get(n: Int, k: Int): Long {
        if (n < k) return 0
        if (n < 0 || k < 0) return 0
//        return fac[n] * (finv[k] * finv[n - k] % mod) % mod
        return fac[n] * (finv[k] * finv[n - k] % mod)
    }
}

fun readString() = readLine()!!
fun readStringList() = readLine()!!.split(" ")
fun readInt() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readIntList() = readLine()!!.split(" ").map(String::toInt)
fun readLongList() = readLine()!!.split(" ").map(String::toLong)