Problem Statement

We have a sequence of positive integers of length $N^2$, $A=(A_1,\ A_2,\ \dots,\ A_{N^2})$, and a positive integer $S$. For this sequence of positive integers, $A_i=A_{i+N}$ holds for positive integers $i\ (1\leq i \leq N^2-N)$, and only $A_1,\ A_2,\ \dots,\ A_N$ are given as the input.

Find the minimum integer $L$ such that every sequence $B$ of positive integers totaling $S$ is a (not necessarily contiguous) subsequence of the sequence $(A_1,\ A_2,\ \dots,\ A_L)$ of positive integers.

It can be shown that at least one such $L$ exists under the Constraints of this problem.

Constraints

• $1 \leq N \leq 1.5 \times 10^6$
• $1 \leq S \leq \min(N,2 \times 10^5)$
• $1 \leq A_i \leq S$
• For every positive integer $x\ (1\leq x \leq S)$, $(A_1,\ A_2,\ \dots,\ A_N)$ contains at least one occurrence of $x$.
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

N S
A_1 A_2 \dots A_N

Output

Print the answer.