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Problem Statement

You are given a permutation $P=(P_1,\ldots,P_N)$ of $(1,\ldots,N)$, and an integer $K$.

Find the number of pairs of integers $(L, R)$ that satisfy all of the following conditions:

• $1 \leq L \leq R \leq N$

• $\mathrm{max}(P_L,\ldots,P_R) - \mathrm{min}(P_L,\ldots,P_R) \leq R - L + K$

Constraints

• $1 \leq N \leq 1.4\times 10^5$
• $P$ is a permutation of $(1,\ldots,N)$.
• $0 \leq K \leq 3$
• All values in input are integers.

Sample Input 1

4 1
1 4 2 3

Sample Output 1

9

The following nine pairs $(L, R)$ satisfy the conditions.

• $(1,1)$
• $(1,3)$
• $(1,4)$
• $(2,2)$
• $(2,3)$
• $(2,4)$
• $(3,3)$
• $(3,4)$
• $(4,4)$

For $(L,R) = (1,2)$, we have $\mathrm{max}(A_1,A_2) -\mathrm{min}(A_1,A_2) = 4-1 = 3$ and $R-L+K=2-1+1 = 2$, not satisfying the condition.

Sample Input 2

2 0
2 1

Sample Output 2

3

Sample Input 3

10 3
3 7 10 1 9 5 4 8 6 2

Sample Output 3

37