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



Sample input:
3 2


Sample output:
2

Submission status: Time Limit Exceeded

Solution code:
def main():

    """ convenient functions
    # for i, a in enumerate(iterable)
    # q, mod = divmod(a, b)
    # divmod(x, y) returns the tuple (x//y, x%y)
    # Higher-order function: reduce(operator.mul, xyz_count, 1)
    # manage median(s) using two heapq https://atcoder.jp/contests/abc127/tasks/abc127_f
    """

    """convenient decorator
    # @functools.lru_cache():
    # to facilitate use of recursive function
        # ex:
        # from functools import lru_cache
        # import sys
        # sys.setrecursionlimit(10**9)
        # @lru_cache(maxsize=None)
        # def fib(n):
        #     if n < 2:
        #         return n
        #     return fib(n-1) + fib(n-2)
        # print(fib(1000))
    """
    
    # import numpy as np
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product # https://docs.python.org/ja/3/library/itertools.html
    # accumulate() returns iterator! to get list: list(accumulate())
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  # prime factor
        b, e = 2, 0  # base, exponent
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        # TODO: How should I do when n - r is negative?
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict # https://docs.python.org/ja/3/library/collections.html#collections.deque
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest # https://docs.python.org/ja/3/library/heapq.html
    from copy import deepcopy, copy # https://docs.python.org/ja/3/library/copy.html
    import operator
    from operator import itemgetter
    # ex1: List.sort(key=itemgetter(1))
    # ex2: sorted(tuples, key=itemgetter(1,2))
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd # Deprecated since version 3.5: Use math.gcd() instead.
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)

    # first create factorial_list
    # fac_list = mod_factorial_list(n)
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    modpow = lambda a, n, p = MOD: pow(a, n, p) # Recursive function in python is slow!
    def modinv(a, p = MOD):
        # evaluate reciprocal using Fermat's little theorem:
        # a**(p-1) is identical to 1 (mod p) when a and p is coprime
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        # fac_list = modfactorial_list(100)
        # print(modcomb(100, 5, modfactorial_list(100)))
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    """ initialize variables and set inputs
    # initialize variables
        # to initialize list, use [0] * n
        # to initialize two dimentional array, use [[0] * N for _ in range(N)]
    # set inputs
        # open(0).read() is a convenient method:
        # ex) n, m, *x = map(int, open(0).read().split())
        #     min(x[::2]) - max(x[1::2])
        # ex2) *x, = map(int, open(0).read().split())
        #     don't forget to add comma after *x if only one variable is used
    # preprocessing
        # transpose = [x for x in zip(*data)]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [(1, 4, 7), (2, 5, 8), (3, 6, 9)]
        # flat = [flatten for inner in data for flatten in inner]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [1, 2, 3, 4, 5, 6, 7, 8, 9]
    # calculate and output
        # output pattern
        # ex1) print(*l) => when l = [2, 5, 6], printed 2 5 6
    """

    # functions used
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    R = lambda: list(map(int, r().split()))
    Rmap = lambda: map(int, r().split())
    Rfloat = lambda: list(map(float, r().split()))
    Rtuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    # single int: int(r())
    # single string: r()
    # single float: float(r())
    # line int: R()
    # line string: r().split()
    # line (str, int, int): [j if i == 0 else int(j) for i, j in enumerate(r().split())]
    # lines int: [R() for _ in range(n)]
    """

    if __name__ != '__main__':
        # for test
        sys.stdin = open('sample.txt')

    # ----------------------------------
    # main

    # N, K = R()
    # dp = [[[0]*3100 for _ in range(51)] for _ in range(51)]
    # dp[0][0][0] = 1
    # for i, rest, k in product(range(N), range(N), range(K+1)):
    #     if k % 2:
    #         continue
    #     dp[i+1][rest+1][k+2*rest+2] += dp[i][rest][k]
    #     dp[i+1][rest+1][k+2*rest+2] %= MOD
    #     # if rest:
    #     #     dp[i+1][rest][k+2*rest] += dp[i][rest][k] * 2 * rest
    #     #     dp[i+1][rest][k+2*rest] %= MOD
    #     dp[i+1][rest][k+2*rest] += dp[i][rest][k] * (2*rest+1)
    #     dp[i+1][rest][k+2*rest] %= MOD
    #     if rest:
    #         dp[i+1][rest-1][k+2*rest-2] += dp[i][rest][k] * rest * rest
    #         dp[i+1][rest-1][k+2*rest-2] %= MOD
    # print(dp[N][0][K])
    
    N, K = R()
    dp = [0]*3100*51*51
    ip = 3100*51
    restp = 3100
    dp[0] = 1
    for i, rest, k in product(range(N), range(N), range(K+1)):
        if k % 2:
            continue
        dp[(i+1)*ip+(rest+1)*restp+(k+2*rest+2)] += dp[i*ip+rest*restp+k]
        dp[(i+1)*ip+(rest+1)*restp+(k+2*rest+2)] %= MOD

        dp[(i+1)*ip+rest*restp+(k+2*rest)] += dp[i*ip+rest*restp+k] * (2*rest+1)
        dp[(i+1)*ip+rest*restp+(k+2*rest)] %= MOD
        if rest:
            dp[(i+1)*ip+(rest-1)*restp+(k+2*rest-2)] += dp[i*ip+rest*restp+k] * rest * rest
            dp[(i+1)*ip+(rest-1)*restp+(k+2*rest-2)] %= MOD
    print(dp[N*ip+K])
    
    # end of main
    # ----------------------------------

    """memo: how to use defaultdict of list
    # initialize
    Dic = defaultdict(list)
    # append / extend
    Dic[x].append(y)
    # for
    for k, v in Dic.items():
    """

if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
def main():

    """ convenient functions
    # for i, a in enumerate(iterable)
    # q, mod = divmod(a, b)
    # divmod(x, y) returns the tuple (x//y, x%y)
    # Higher-order function: reduce(operator.mul, xyz_count, 1)
    # manage median(s) using two heapq https://atcoder.jp/contests/abc127/tasks/abc127_f
    """

    """convenient decorator
    # @functools.lru_cache():
    # to facilitate use of recursive function
        # ex:
        # from functools import lru_cache
        # import sys
        # sys.setrecursionlimit(10**9)
        # @lru_cache(maxsize=None)
        # def fib(n):
        #     if n < 2:
        #         return n
        #     return fib(n-1) + fib(n-2)
        # print(fib(1000))
    """
    
    # import numpy as np
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product # https://docs.python.org/ja/3/library/itertools.html
    # accumulate() returns iterator! to get list: list(accumulate())
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  # prime factor
        b, e = 2, 0  # base, exponent
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        # TODO: How should I do when n - r is negative?
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict # https://docs.python.org/ja/3/library/collections.html#collections.deque
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest # https://docs.python.org/ja/3/library/heapq.html
    from copy import deepcopy, copy # https://docs.python.org/ja/3/library/copy.html
    import operator
    from operator import itemgetter
    # ex1: List.sort(key=itemgetter(1))
    # ex2: sorted(tuples, key=itemgetter(1,2))
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd # Deprecated since version 3.5: Use math.gcd() instead.
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)

    # first create factorial_list
    # fac_list = mod_factorial_list(n)
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    modpow = lambda a, n, p = MOD: pow(a, n, p) # Recursive function in python is slow!
    def modinv(a, p = MOD):
        # evaluate reciprocal using Fermat's little theorem:
        # a**(p-1) is identical to 1 (mod p) when a and p is coprime
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        # fac_list = modfactorial_list(100)
        # print(modcomb(100, 5, modfactorial_list(100)))
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    """ initialize variables and set inputs
    # initialize variables
        # to initialize list, use [0] * n
        # to initialize two dimentional array, use [[0] * N for _ in range(N)]
    # set inputs
        # open(0).read() is a convenient method:
        # ex) n, m, *x = map(int, open(0).read().split())
        #     min(x[::2]) - max(x[1::2])
        # ex2) *x, = map(int, open(0).read().split())
        #     don't forget to add comma after *x if only one variable is used
    # preprocessing
        # transpose = [x for x in zip(*data)]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [(1, 4, 7), (2, 5, 8), (3, 6, 9)]
        # flat = [flatten for inner in data for flatten in inner]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [1, 2, 3, 4, 5, 6, 7, 8, 9]
    # calculate and output
        # output pattern
        # ex1) print(*l) => when l = [2, 5, 6], printed 2 5 6
    """

    # functions used
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    R = lambda: list(map(int, r().split()))
    Rmap = lambda: map(int, r().split())
    Rfloat = lambda: list(map(float, r().split()))
    Rtuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    # single int: int(r())
    # single string: r()
    # single float: float(r())
    # line int: R()
    # line string: r().split()
    # line (str, int, int): [j if i == 0 else int(j) for i, j in enumerate(r().split())]
    # lines int: [R() for _ in range(n)]
    """

    if __name__ != '__main__':
        # for test
        sys.stdin = open('sample.txt')

    # ----------------------------------
    # main

    N, K = R()
    dp = [[[0]*3100 for _ in range(51)] for _ in range(51)]
    dp[0][0][0] = 1
    for i, rest, k in product(range(N), range(N), range(K+1)):
        dp[i+1][rest+1][k+2*rest+2] = (dp[i+1][rest+1][k+2*rest+2] + dp[i][rest][k]) % MOD
        if rest:
            dp[i+1][rest][k+2*rest] = (dp[i+1][rest][k+2*rest] + dp[i][rest][k] * 2 * rest) % MOD
        dp[i+1][rest][k+2*rest] = (dp[i+1][rest][k+2*rest] + dp[i][rest][k]) % MOD
        if rest:
            dp[i+1][rest-1][k+2*rest-2] = (dp[i+1][rest-1][k+2*rest-2] + dp[i][rest][k] * rest * rest) % MOD
    print(dp[N][0][K])
    
    
    # end of main
    # ----------------------------------

    """memo: how to use defaultdict of list
    # initialize
    Dic = defaultdict(list)
    # append / extend
    Dic[x].append(y)
    # for
    for k, v in Dic.items():
    """

if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
n, k = map(int, input().split())
md = 10 ** 9 + 7
if k % 2:
    print(0)
    exit()
k //= 2
dp = [[[0] * (n ** 2) for _ in range(n + 2)] for __ in range(n + 1)]
dp[0][0][0] = 1
for i in range(1, n + 1):
    dpi1 = dp[i - 1]
    for j in range(i + 1):
        for s in range(j, k + 1):
            # 片側、水平、両方上
#            print(i,j,s)
            tmp = dpi1[j][s - j] * j * 2 + dpi1[j][s - j] + dpi1[j + 1][s - j] * (j + 1) ** 2
            if j:
                # 両方保留
                tmp += dp[i - 1][j - 1][s - j]
            dp[i][j][s] = tmp % md
print(dp[n][0][k])

Submission status: Time Limit Exceeded

Solution code:
MOD = 10**9 + 7
n, oddness = [int(item) for item in input().split()]
# Oddness must be even
if oddness % 2 ==  1:
    print(0)
    exit()
oddness //= 2
max_oddness = 1250 + n
max_pending = n//2 + 2

dp = [[[0] * (max_oddness) for _ in range(max_pending)] for _ in range(n)]
dp[0][0][0] = 1
dp[0][1][1] = 1
for i in range(1, n):
    for j in range(min(i+1, n//2+1)):
        for k in range(oddness+1):
            # Oddness increase by num of pending item
            # Connect in line 
            dp[i][j][k+j] += dp[i-1][j][k]
            # Choose 1 from pending items
            dp[i][j][k+j] += dp[i-1][j][k] * j * 2
            dp[i][j][k+j] %= MOD
            # Choose 2 from pending items
            if j > 0:
                dp[i][j-1][k+j-1] += dp[i-1][j][k] * j*j
            # Do nothing 
            dp[i][j+1][k+j+1] += dp[i-1][j][k] 

print(dp[n-1][0][oddness] % MOD)

Submission status: Time Limit Exceeded

Solution code:
MOD = 10**9 + 7
n, oddness = [int(item) for item in input().split()]
# Oddness must be even
if oddness % 2 ==  1:
    print(0)
    exit()
oddness //= 2
max_oddness = 1300 + n
max_pending = n + 1

dp = [[[0] * (max_oddness) for _ in range(max_pending)] for _ in range(n)]
dp[0][0][0] = 1
dp[0][1][1] = 1
for i in range(1, n):
    for j in range(i+1):
        # Too many pending items 
        if j > n // 2:
            break
        for k in range(1300):
            # Connect in line
            # Oddness increase by num of pending item
            dp[i][j][k+j] += dp[i-1][j][k]
            # Choose 1 from pending items
            dp[i][j][k+j] += dp[i-1][j][k] * j*2 
            dp[i][j][k+j] %= MOD
            # Choose 2 from pending items
            if j > 0:
                dp[i][j-1][k+j-1] += dp[i-1][j][k] * j*j
                dp[i][j-1][k+j-1] %= MOD 
            # Do nothing 
            dp[i][j+1][k+j+1] += dp[i-1][j][k] 
            dp[i][j+1][k+j+1] %= MOD 

print(dp[n-1][0][oddness])

Submission status: Time Limit Exceeded

Solution code:
MOD = 10**9 + 7
n, oddness = [int(item) for item in input().split()]
# Oddness must be even
if oddness % 2 ==  1:
    print(0)
    exit()
oddness //= 2
max_oddness = n*n + n
max_pending = n + 1

dp = [[[0] * (max_oddness) for _ in range(max_pending)] for _ in range(n)]
dp[0][0][0] = 1
dp[0][1][1] = 1
oddness_itr = [item for item in range(n*n)]
for i in range(1, n):
    for j in range(i+1):
        # Too many pending items 
        if j > n // 2:
            break
        for k in oddness_itr:
            # Connect in line
            # Oddness increase by num of pending item
            dp[i][j][k+j] += dp[i-1][j][k]
            # Choose 1 from pending items
            dp[i][j][k+j] += dp[i-1][j][k] * j*2 
            dp[i][j][k+j] %= MOD
            # Choose 2 from pending items
            if j > 0:
                dp[i][j-1][k+j-1] += dp[i-1][j][k] * j*j
                dp[i][j-1][k+j-1] %= MOD 
            # Do nothing 
            dp[i][j+1][k+j+1] += dp[i-1][j][k] 
            dp[i][j+1][k+j+1] %= MOD 

print(dp[n-1][0][oddness])

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-
import bisect
import heapq
import math
import random
import sys
from collections import Counter, defaultdict, deque
from decimal import ROUND_CEILING, ROUND_HALF_UP, Decimal
from functools import lru_cache, reduce
from itertools import combinations, combinations_with_replacement, product, permutations
from operator import add, mul, sub

sys.setrecursionlimit(100000)
input = sys.stdin.readline


def read_int():
    return int(input())


def read_int_n():
    return list(map(int, input().split()))


def read_float():
    return float(input())


def read_float_n():
    return list(map(float, input().split()))


def read_str():
    return input().strip()


def read_str_n():
    return list(map(str, input().split()))


def error_print(*args):
    print(*args, file=sys.stderr)


def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap


@mt
def slv(N, K):
    M = 10**9 + 7
    @lru_cache(maxsize=None)
    def f(l, k):
        # error_print(len(l))
        if len(l) == 0:
            if k == K:
                return 1
            else:
                return 0
        if k > K:
            return 0

        i = N - len(l) + 1
        ans = 0
        for n in l:
            ll = list(l)
            ll.remove(n)
            ans = (ans + f(tuple(ll), k + abs((n - i)))) % M
        return ans
    return f(tuple(range(1, N+1)), 0)


def main():
    N, K = read_int_n()
    print(slv(N, K))


if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
N, k = map(int, input().split())

def calcul_kimyo(perm):
  perm = list(map(int, perm))
  kimyo = 0
  for i, p in enumerate(perm):
    kimyo += abs(i+1-p)
  return kimyo

import itertools

pool = map(str, list(range(1, N+1, 1)))
perm_list = list(itertools.permutations(pool))

kimyo_count = 0
for perm in perm_list:
  if calcul_kimyo(perm) == k:
    kimyo_count +=1

ans = str(int(kimyo_count % (10e9 + 7)))
print(ans)

Submission status: Time Limit Exceeded

Solution code:
import itertools
n, k = map(int,input().split())
per=list(itertools.permutations([i+1 for i in range(n)]))
s=0
for i in range(len(per)):
    oddness=0
    for j,value in enumerate(per[i]):
        oddness+=abs(j+1-value)
    if k==oddness:
        s+=1
print(s%(10**9+7))

Submission status: Time Limit Exceeded

Solution code:
import sys
def input():
    return sys.stdin.readline()[:-1]
n, k = map(int, input().split())
div = 10**9 + 7

cnt = 0
setn = tuple(i for i in range(1, n+1))

import itertools as itr
for perm in itr.permutations(setn):
    sumv = 0
    for i, pi in enumerate(perm):
        sumv += abs(i+1-pi)

    if sumv == k:
        cnt += 1
        cnt = (cnt%div)


print(cnt%div)

Submission status: Time Limit Exceeded

Solution code:
import itertools
n, k = map(int, input().split() )
ps=list(itertools.permutations(range(n) ) )
odds = [sum([abs(s-p.index(s)) for s in p]) for p in ps]
judge=sum([1 for s in odds if s==k])%(10**9+7)
print(judge)

Submission status: Time Limit Exceeded

Solution code:
import itertools
n, k = map(int, input().split() )
ps=list(itertools.permutations(range(n) ) )
judge=0
for p in ps:
    odd=[abs(s-p.index(s)) for s in p]
    if sum(odd)==k:
        judge+=1
print(judge%(10**9+7))

Submission status: Time Limit Exceeded

Solution code:
import numpy as np
import itertools

def oddness(p):
  odd = 0
  for i, pi in enumerate(p):
    odd += abs(i+1-pi)
  return odd

n, k = map(int, input().split(" "))
n = [x for x in range(1, n+1)]
count = 0
for p in list(itertools.permutations(n)):
  if k == oddness(p):
    count += 1
print(count%(1000000007))

Submission status: Time Limit Exceeded

Solution code:
import numpy as np
import itertools

def oddness(p):
  odd = 0
  for i, pi in enumerate(p):
    odd += abs(i+1-pi)
  return odd

n, k = map(int, input().split(" "))
n = [x for x in range(1, n+1)]
count = 0
for p in list(itertools.permutations(n)):
  if k == oddness(p):
    count += 1
print(count)

Submission status: Time Limit Exceeded

Solution code:
import itertools
n,k = map(int,input().rstrip().split(' '))
p = [i+1 for i in range(n)]
p1 = list(itertools.permutations(p))
r = 0
for j in p1:
        s = 0
        for i in p:
               s += abs(i - j[i-1]) 
        if s == k:
                r += 1
print(r)

Submission status: Time Limit Exceeded

Solution code:
N, K = map(int, raw_input().split())

A = [i + 1 for i in xrange(N)]

def permute(ind):
    if ind >= N:
        s = 0
        for i in xrange(N): s += abs(i + 1 - A[i])
        if s not in ans: ans[s] = 0
        ans[s] += 1
    else:
        for i in range(ind, N):
            A[i], A[ind] = A[ind], A[i]
            permute(ind + 1)
            A[i], A[ind] = A[ind], A[i]

ans = {}
permute(0)

print ans[K] if K in ans else 0

Submission status: Time Limit Exceeded

Solution code:
from itertools import permutations

n, k = map(int, input().split())
p = list(permutations(list(range(1, n+1))))
mod = 10**9 + 7
def getOddness(l):
    ans = 0
    for i in range(n):
        ans += abs(i-l[i]+1)
    return ans


count = 0
for i in p:
    if k == getOddness(i):
        count += 1

print(count%mod)