Problem I
Deterministic Finite Automata - Is the Empty Language?

You are given a deterministic finite automaton that accepts the language $\mathcal{L}$. You should output whether $\mathcal{L}$ is the empty language.

Input

The input contains the description of a deterministic finite automaton.

The first line contains four positive integers $n$, $c$, $s$, and $f$, where $n$ is the number of states, $c$ is the size of the alphabet, $s$ is the initial state, and $f$ is the number of final states. The second line consists of a string $\Sigma = \Sigma _1\Sigma _2\dots \Sigma _c$ of $c$ distinct symbols, each of which is a lowercase english character. The third line consists of $f$ distinct positive integers, the set of final states. Then $n$ lines follow, each with $c$ positive integers, describing the symbol table. The $j$-th integer on the $i$-th of those lines represents the state transitioned to from state $i$ upon reading $\Sigma _j$.

Each state is an integer between $1$ and $n$. It is guaranteed that $1 \leq n \leq 10\, 000$, $1 \leq s \leq n$, and $0 \leq f \leq n$.

Output

Output empty if $\mathcal{L}$ is the empty language, otherwise output non-empty.

3 2 1 1
ab
2
2 3
3 2
3 3

non-empty

2 4 1 1
acgt
2
1 1 1 1
1 2 2 1

empty