There is a simple directed graph G with $N$ vertices, numbered $1,2,…,N$.
For each $i$ and $j\ (1≤i,j≤N)$, 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 is given from Standard Input in the following format:
$N\ K$
$a_{1, 1}\ \ldots\ a_{1, N}$
$:$
$a_{N, 1}\ \ldots\ a_{N, N}$

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

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

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

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

1

G is drawn in the figure below:

There is one directed path of length 2:

• 4 → 5 → 6