Too Many Initializer Elements

Source: Phuoc Hung OJ

Version: Phuoc Hung OJ Extended

Problem

A conceptual fixed-capacity C declaration is

int a[N] = {v0, v1, ..., v(K-1)};

Here $N$ denotes a positive integer constant in the declaration and the initializer list contains exactly $K$ elements. The declaration is valid when $K\le N$; when $K<N$, the remaining elements are zero-initialized. If $K>N$, there are excess initializers and the declaration is invalid.

Input

The first line contains $N,K$. The second line contains exactly $K$ initializer values.

Output

Print VALID if $K\le N$; otherwise print INVALID.

Subtask

Subtask 1 (20 points): $1\le N,K\le10$.

Subtask 2 (30 points): $1\le N,K\le100$.

Subtask 3 (50 points): $1\le N,K\le1000$.

Example

Input

3 4
1 2 3 4

Output

INVALID

Explanation

$K=4>N=3$, so the initializer list is too long.