Financial Report

JOI mart is a shop with N days of history. After it opened, the sales amount on the i-th day (1 ≤ i ≤ N) was $A_i$ yen.

Bitaro is the shop manager of JOI mart. He will make a presentation of the financial report. He chooses some days and shows a bar chart of their sales amounts in chronological order, then explains how the sales changed over those days. He wants the presentation to leave a strong impression, so he picks the data carefully.

Suppose he chooses the sales data for $m$ days (1 ≤ m ≤ N), namely days $p_1, p_2, \ldots, p_m$ after opening, where $1 \le p_1 < p_2 < \cdots < p_m \le N$. The impression score of the bar chart is the number of indices $j$ (1 ≤ j ≤ m) such that $j = 1$ or $\max\{A_{p_1}, A_{p_2}, \ldots, A_{p_{j-1}}\} < A_{p_j}$. In other words, it counts how many chosen days set a new record-high sales amount.

Bitaro must satisfy both conditions:

• He shows the latest sales amount, so $p_m = N$.
• For consecutive chosen days, the gap is at most D days. If $m \ge 2$, then $p_{j+1} - p_j \le D$ for every $1 \le j \le m-1$.

Given the sales data and D, find the maximum impression score over all valid choices.

Read the following data from standard input. All values are integers.

N D
A_1 A_2 ... A_N

Write one line to standard output containing the maximum impression score.

• 1 ≤ N ≤ 300000.
• 1 ≤ D ≤ N.
• 0 ≤ $A_i$ ≤ 1000000000 (1 ≤ i ≤ N).