Background

Little Z wants to grind whk.

Problem Description

Little Z needs to grind a total of $n$ subjects. For the $i$-th subject, he has one and only $a_i$ problems. There are infinitely many days available, and each day Little Z can solve infinitely many problems.

If Little Z considers a day to be interesting, it is only when on that day he solves problems from at least $t$ subjects.

Little Z wants to know the maximum number of interesting days.

Input Format

The first line contains $2$ positive integers $n, t$.

The next line contains $n$ integers: $a_1, a_2, a_3, \dots, a_{n-1}, a_n$.

Output Format

Output one integer, the maximum number of days that Little Z considers interesting.

5 3 
3 2 5 1 1 

3 

6 4 
1 1 4 5 1 4 

3 

Hint

Subtask 0 is hack testdata and is not scored.

This problem uses bundled tests.

Constraints: for all testdata, $1\le t\le n\le 5\times10^5$, $1\le a_i \le 10^6$.

Translated by ChatGPT 5