Problem:
Score : 600 points

Problem Statement

Let us define the oddness of a permutation p = {p_1,\ p_2,\ ...,\ p_n} of {1,\ 2,\ ...,\ n} as \sum_{i = 1}^n |i - p_i|.

Find the number of permutations of {1,\ 2,\ ...,\ n} of oddness k, modulo 10^9+7.

Constraints

All values in input are integers.

1 \leq n \leq 50

0 \leq k \leq n^2

Input

Input is given from Standard Input in the following format:

n k

Output

Print the number of permutations of {1,\ 2,\ ...,\ n} of oddness k, modulo 10^9+7.

Sample Input 1

3 2

Sample Output 1

2

There are six permutations of {1,\ 2,\ 3}. Among them, two have oddness of 2: {2,\ 1,\ 3} and {1,\ 3,\ 2}.

Sample Input 2

39 14

Sample Output 2

74764168

Solution in Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc, wr = bufio.NewScanner(os.Stdin), bufio.NewWriter(os.Stdout)

func scanString() string   { sc.Scan(); return sc.Text() }
func scanRunes() []rune    { return []rune(scanString()) }
func scanInt() int         { a, _ := strconv.Atoi(scanString()); return a }
func scanInt64() int64     { a, _ := strconv.ParseInt(scanString(), 10, 64); return a }
func scanFloat64() float64 { a, _ := strconv.ParseFloat(scanString(), 64); return a }

func scanInts(n int) []int {
	res := make([]int, n)
	for i := 0; i < n; i++ {
		res[i] = scanInt()
	}
	return res
}

func debug(a ...interface{}) { fmt.Fprintln(os.Stderr, a...) }

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}
func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}
func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

//•*¨*•.¸¸♪main•*¨*•.¸¸♪(　-ω-)ノ　(　・ω・)
func main() {
	defer wr.Flush()
	sc.Split(bufio.ScanWords)
	sc.Buffer(make([]byte, 10000), 1001001)

	n := scanInt()
	k := scanInt()

	dp := [60][60][10000]int{}
	dp[0][0][0] = 1
	for i := 0; i < n; i++ {
		for j := 0; j < i+1; j++ {
			for x := 0; x < k+1; x++ {
				if j > 0 {
					dp[i+1][j-1][x+(j-1)*2] += dp[i][j][x]*j*j%MOD
					dp[i+1][j-1][x+(j-1)*2] %= MOD
				}
				dp[i+1][j][x+j*2] += dp[i][j][x] + dp[i][j][x]*j*2%MOD
				dp[i+1][j][x+j*2] %= MOD
				dp[i+1][j+1][x+(j+1)*2] += dp[i][j][x]
				dp[i+1][j+1][x+(j+1)*2] %= MOD
			}
		}
	}

	fmt.Fprintln(wr, dp[n][0][k])
}

// MOD constant
const MOD = 1000000007