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.

Sample Input 1

6 4
1 1 2 1 4 3

Sample Output 1

9

There are eight sequences $B$ to consider: $B=(1,\\ 1,\\ 1,\\ 1),\\ (1,\\ 1,\\ 2),\\ (1,\\ 2,\\ 1),\\ (1,\\ 3),\\ (2,\\ 1,\\ 1),\\ (2,\\ 2),\\ (3,\\ 1),\\ (4)$.

For $L=8$, for instance, $B=(2,\\ 2)$ is not a subsequence of $(A_1,A_2,\\ \\dots,\\ A_8)=(1,\\ 1,\\ 2,\\ 1,\\ 4,\\ 3,\\ 1,\\ 1)$.

For $L=9$, on the other hand, every $B$ is a subsequence of $(A_1,A_2,\\ \\dots,\\ A_9)=(1,\\ 1,\\ 2,\\ 1,\\ 4,\\ 3,\\ 1,\\ 1,\\ 2)$.

Sample Input 2

14 5
1 1 1 2 3 1 2 4 5 1 1 2 3 1

Sample Output 2

11

Sample Input 3

19 10
1 6 2 7 4 8 5 9 1 10 4 1 3 1 3 2 2 2 1

Sample Output 3

39