Migrated from Lutece 1860 Will the circle be broken

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Description

You are given an array $A$ of $N$ non-negative integers and an integer $M$.

Find the number of pair$(i,j)$ such that $1 \leq i \leq j \leq N$ and $\min(A_i,A_{i+1},...,A_j) \cdot (A_i \oplus A_{i+1} \oplus ... \oplus A_j ) \leq M$.

Input

The first line contains two integers $N$ $(1 \leq N \leq 10^5)$ and $M$ $(0 \leq M \leq 10^{18})$.

The second line contains $N$ integers representing the elements of $A_i$ $(1 \leq A_i \leq 10^9)$.

Output

Print the corresponding answer in a single line.

Samples

4 2
1 4 772002 200277

1

5 3
1 2 3 2 1

11

Resources

The 16th UESTC Programming Contest Preliminary