Problem Statement

There are $N$ cities. The time it takes to travel from City $i$ to City $j$ is $T_{i, j}$.

Among those paths that start at City $1$, visit all other cities exactly once, and then go back to City $1$, how many paths take the total time of exactly $K$ to travel along?

Constraints

• $2\leq N \leq 8$
• If $i\neq j$, $1\leq T_{i,j} \leq 10^8$.
• $T_{i,i}=0$
• $T_{i,j}=T_{j,i}$
• $1\leq K \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
T_{1,1} \ldots T_{1,N}
\vdots
T_{N,1} \ldots T_{N,N}

Output

Print the answer as an integer.