Training Site

Totem Pole

Input: Standard Input (stdin)
Output: Standard Output (stdout)
Memory limit: 32 megabytes
Time limit: 1.0 seconds

A group of $N$ people ($1 \le N \le 100{,}000$) are standing in a line to make carvings on a totem pole. The totem pole has $T$ positions ($1 \le T \le 100{,}000$) where carvings can be made, at heights $1, 2, ..., T$.

The $i$-th person has height $H_i$ ($1 \le H_i \le 100{,}000$), and can only make a carving at heights up to $H_i$.

Each person in turn will make a carving at the highest position they can at which a carving hasn't been made yet. There may be no such position, in which case the person won't make a carving and will be sad.

Your task is to determine the number of people who will make carvings.

Input

The first line will contain two space-separated integers, $N$ and $T$. The second line will contain $N$ space-separated integers, the heights of the people in the order they will make the carvings.

Output

Output a single integer, the number of people who will make carvings.

• Subtask 1 (40%): $1 \le N, T, H_i \le 1{,}000$
• Subtask 2 (10%): $1 \le N, T \le 1{,}000$
• Subtask 3 (50%): $1 \le N, T \le 100{,}000$

Sample Explanation

The first three people make carvings at heights 2, 3, and 1. The fourth person can't make a carving because all the positions they can reach already have carvings. The last person makes a carving at height 4.

• Sample Input 1

5 4
2 3 2 3 6


Sample Output 1

4