Counting of Subarrays

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.

Examples

Input

9 3 2 1 1 1 1 1 1 2 3

Output

22

Input

9 2 2 1 1 1 1 1 1 2 3

Output

41

Input

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

Output

31

inputFormat

Input

Input is given from Standard Input in the following format:

N L A_1 A_2 ... A_N

outputFormat

Output

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

Examples

Input

9 3 2 1 1 1 1 1 1 2 3

Output

22

Input

9 2 2 1 1 1 1 1 1 2 3

Output

41

Input

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

Output

31

样例

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

31