You are given an array $A$ of $N$ integers: $[A_1, A_2, \dots, A_N]$.

The array $A$ is $(p, q)$-xorderable if it is possible to rearrange $A$ such that for each pair $(i, j)$ that satisfies $1 \leq i < j \leq N$, the following conditions must be satisfied after the rearrangement: $A_i \oplus p \leq A_j \oplus q$ and $A_i \oplus q \leq A_j \oplus p$. The operator $\oplus$ represents the bitwise xor.

You are given another array $X$ of length $M$: $[X_1, X_2, \dots, X_M]$. Calculate the number of pairs $(u, v)$ where array $A$ is $(X_u, X_v)$-xorderable for $1 \leq u < v \leq M$.

Input

The first line consists of two integers $N$ $M$ ($2 \leq N, M \leq 200\,000)$.

The second line consists of $N$ integers $A_i$ ($0 \leq A_i < 2^{30})$.

The third line consists of $M$ integers $X_u$ ($0 \leq X_u < 2^{30})$.

Output

Output a single integer representing the number of pairs $(u, v)$ where array $A$ is $(X_u, X_v)$-xorderable for $1 \leq u < v \leq M$.

见题面 Input 部分

见题面 Output 部分

Explanation for the sample input/output #1

The array $A$ is $(1, 1)$-xorderable by rearranging the array $A$ to $[0, 0, 3]$.

Explanation for the sample input/output #2

The array $A$ is $(12, 10)$-xorderable by rearranging the array $A$ to $[13, 0, 7, 24, 22]$.