Shashank loves longest increasing subsequence. A subsequence, 1 ≤ i₁ < i₂ < ... < i_k ≤ n is called increasing if A[i₁]  ≤ A[i₂]  ≤ A[i₃]  ≤ ...  ≤ A[i_k]. An increasing subsequence is called longest if it has maximum length among all increasing subsequences.

Shashank added one more restriction that the chosen indexes atleast differ by D. i.e. i_j - i_j-1 ≥ D for all j ≥ 1.

Help Shashank by finding length of LIS after the added restriction.

Input Format

First line contains two space separated integers n and D
Second line contains n space separating integers which are the elements of array A as defined above.

Output Format

Output a single integer, which is answer to the problem

Constraints

• 1 ≤ n, A[i] ≤ 100000