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 $$$1 \leq i \lt j \leq N$$$, 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 $$$1 \leq u \lt v \leq M$$$.

Input

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

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

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

Output

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

Note

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 $$$[13, 0, 7, 24, 22]$$$.

Xorderable Array

Examples