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.

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.

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

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.

见题面 Input 部分

见题面 Output 部分