Score : $1800$ points

Problem Statement

For a sequence $S$ of positive integers and positive integers $k$ and $l$, $S$ is said to belong to level $(k,l)$ when one of the following conditions is satisfied:

• The length of $S$ is $1$, and its only element is $k$.
• There exist sequences $T_1,T_2,...,T_m$ ($m \geq l$) belonging to level $(k-1,l)$ such that the concatenation of $T_1,T_2,...,T_m$ in this order coincides with $S$.

Note that the second condition has no effect when $k=1$, that is, a sequence belongs to level $(1,l)$ only if the first condition is satisfied.

Given are a sequence of positive integers $A_1,A_2,...,A_N$ and a positive integer $L$. Find the number of subsequences $A_i,A_{i+1},...,A_j$ ($1 \leq i \leq j \leq N$) that satisfy the following condition:

• There exists a positive integer $K$ such that the sequence $A_i,A_{i+1},...,A_j$ belongs to level $(K,L)$.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $2 \leq L \leq N$
• $1 \leq A_i \leq 10^9$

Input

Input is given from Standard Input in the following format:

$N$ $L$

$A_1$ $A_2$ $...$ $A_N$

Output

Print the number of subsequences $A_i,A_{i+1},...,A_j$ ($1 \leq i \leq j \leq N$) that satisfy the condition.

9 3
2 1 1 1 1 1 1 2 3

22

For example, both of the sequences $(1,1,1)$ and $(2)$ belong to level $(2,3)$, so the sequence $(2,1,1,1,1,1,1)$ belong to level $(3,3)$.

9 2
2 1 1 1 1 1 1 2 3

41

15 3
4 3 2 1 1 1 2 3 2 2 1 1 1 2 2

31