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: Accepted)

fun main(args: Array<String>) {
    val (r1, c1, r2, c2) = readLine()!!.split(" ").map(String::toInt)
    val combi = Combination(2000002)
    val ans = combi(r2 + c2 + 2, c2 + 1) - combi(r2 + c1 + 1, c1) - combi(r1 + c2 + 1, c2 + 1) + combi(r1 + c1, c1)
    println(ans)
}

class MInt {
    private val MOD = 1000000007L
    var v: Long

    constructor(v: Long) {
        this.v = v % MOD
    }

    constructor(v: Int) {
        this.v = v.toLong() % MOD
    }

    operator fun plus(b: MInt): MInt {
        val a = MInt(v)
        a += b
        return a
    }

    operator fun minus(b: MInt): MInt {
        val a = MInt(v)
        a -= b
        return a
    }

    operator fun times(b: MInt): MInt {
        val a = MInt(v)
        a *= b
        return a
    }

    operator fun div(b: MInt): MInt {
        val a = MInt(v)
        a /= b
        return a
    }

    operator fun plusAssign(b: MInt) {
        v += b.v
        if (v >= MOD) v -= MOD
    }

    operator fun minusAssign(b: MInt) {
        v -= b.v
        if (v < 0) v += MOD
    }

    operator fun timesAssign(b: MInt) {
        v *= b.v
        v %= MOD
    }

    operator fun divAssign(b: MInt) {
        this *= b.inv()
    }

    fun inv(): MInt {
        var a = v
        var b = MOD
        var u = 1L
        var w = 0L
        while (b != 0L) {
            val t = a / b
            a -= t * b
            u -= t * w
            var tmp = a
            a = b
            b = tmp
            tmp = u
            u = w
            w = tmp
        }
        u %= MOD
        if (u < 0) u += MOD
        return MInt(u)
    }

    fun pow(n: Int): MInt {
        var a = MInt(1)
        for (i in 1..n) a = a * this
        return a
    }

    override fun toString(): String {
        return v.toString()
    }
}

class Combination(n: Int) {
    private val fact = arrayOfNulls<MInt>(n + 1)
    private val ifact = arrayOfNulls<MInt>(n + 1)

    init {
        fact[0] = MInt(1)
        (1..n).forEach { i -> fact[i] = fact[i - 1]!! * MInt(i) }
        ifact[n] = fact[n]!!.inv()
        (n downTo 1).forEach { i -> ifact[i - 1] = ifact[i]!! * MInt(i) }
    }

    operator fun invoke(n: Int, k: Int): MInt {
        if (k < 0 || n < k) return MInt(0)
        return (fact[n]!! * ifact[k]!! * ifact[n - k]!!)
    }
}