Problem:
Score : 100 points

Problem Statement

There is a simple directed graph G with N vertices, numbered 1, 2, \ldots, N.

For each i and j (1 \leq i, j \leq N), you are given an integer a_{i, j} that represents whether there is a directed edge from Vertex i to j.
If a_{i, j} = 1, there is a directed edge from Vertex i to j; if a_{i, j} = 0, there is not.

Find the number of different directed paths of length K in G, modulo 10^9 + 7.
We will also count a path that traverses the same edge multiple times.

Constraints

All values in input are integers.

1 \leq N \leq 50

1 \leq K \leq 10^{18}

a_{i, j} is 0 or 1.

a_{i, i} = 0

Input

Input is given from Standard Input in the following format:

N K
a_{1, 1} \ldots a_{1, N}
:
a_{N, 1} \ldots a_{N, N}

Output

Print the number of different directed paths of length K in G, modulo 10^9 + 7.

Sample Input 1

4 2
0 1 0 0
0 0 1 1
0 0 0 1
1 0 0 0

Sample Output 1

6

G is drawn in the figure below:

There are six directed paths of length 2:

1 → 2 → 3

1 → 2 → 4

2 → 3 → 4

2 → 4 → 1

3 → 4 → 1

4 → 1 → 2

Sample Input 2

3 3
0 1 0
1 0 1
0 0 0

Sample Output 2

3

G is drawn in the figure below:

There are three directed paths of length 3:

1 → 2 → 1 → 2

2 → 1 → 2 → 1

2 → 1 → 2 → 3

Sample Input 3

6 2
0 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 0 0
0 0 0 0 1 0
0 0 0 0 0 1
0 0 0 0 0 0

Sample Output 3

1

G is drawn in the figure below:

There is one directed path of length 2:

4 → 5 → 6

Sample Input 4

1 1
0

Sample Output 4

0

Sample Input 5

10 1000000000000000000
0 0 1 1 0 0 0 1 1 0
0 0 0 0 0 1 1 1 0 0
0 1 0 0 0 1 0 1 0 1
1 1 1 0 1 1 0 1 1 0
0 1 1 1 0 1 0 1 1 1
0 0 0 1 0 0 1 0 1 0
0 0 0 1 1 0 0 1 0 1
1 0 0 0 1 0 1 0 0 0
0 0 0 0 0 1 0 0 0 0
1 0 1 1 1 0 1 1 1 0

Sample Output 5

957538352

Be sure to print the count modulo 10^9 + 7.

Solution in Python (3.8.2) (judge verdict: Wrong Answer)

import sys
sys.setrecursionlimit(1 << 25)
readline = sys.stdin.buffer.readline
read = sys.stdin.readline  # 文字列読み込む時はこっち

import numpy as np
from functools import partial
array = partial(np.array, dtype=np.int64)
zeros = partial(np.zeros, dtype=np.int64)
full = partial(np.full, dtype=np.int64)


def ints(): return np.fromstring(readline(), sep=' ', dtype=np.int64)


def read_matrix(H, W)->np.ndarray:
    '''return np.ndarray shape=(H,W) matrix'''
    lines = []
    for _ in range(H):
        lines.append(read())
    lines = ' '.join(lines)  # byte同士の結合ができないのでreadlineでなくreadで
    return np.fromstring(lines, sep=' ', dtype=np.int64).reshape(H, W)


MOD = 10**9 + 7
INF = 2**31  # 2147483648 > 10**9
# default import

N, K = ints()
A = read_matrix(N, N)

A_double = np.asanyarray(A, dtype='uint64')
ans = np.eye(N, dtype='uint64')
print(A_double.dtype)
for j in range(int(K).bit_length()):
    if (K >> j) & 1:
        ans = (ans@A_double) % MOD
    A_double = (A_double @ A_double) % MOD

a = 0
for i in range(N):
    for j in range(N):
        a += ans[i, j]
        a %= MOD
# print(ans.sum() % MOD)
print(int(a))


# print(np.linalg.matrix_power(A, K))

# from numba import njit
# @njit('(i8,i8,i8[:])',cache=True)