Codeforces Round #340 (Div. 2) E. XOR and Favorite Number 莫队算法

E. XOR and Favorite Number time limit per test 4 seconds memory limit per test 256 megabytes input standard input output standard output

Bob has a favorite number k and ai of length n. Now he asks you to answer m queries. Each query is given by a pair li and ri and asks you to count the number of pairs of integers i and j, such that l ≤ i ≤ j ≤ r and the xor of the numbers ai, ai + 1, …, aj is equal to k. Input

The first line of the input contains integers n, m and k (1 ≤ n, m ≤ 100 000, 0 ≤ k ≤ 1 000 000) — the length of the array, the number of queries and Bob’s favorite number respectively.

The second line contains n integers ai (0 ≤ ai ≤ 1 000 000) — Bob’s array.

Then m lines follow. The i-th line contains integers li and ri (1 ≤ li ≤ ri ≤ n) — the parameters of the i-th query. Output

PRint m lines, answer the queries in the order they appear in the input. Examples Input

6 2 3 1 2 1 1 0 3 1 6 3 5

Output

7 0

Input

5 3 1 1 1 1 1 1 1 5 2 4 1 3

Output

9 4 4

Note

In the first sample the suitable pairs of i and j for the first query are: (1, 2), (1, 4), (1, 5), (2, 3), (3, 6), (5, 6), (6, 6). Not a single of these pairs is suitable for the second query.

In the second sample xor equals 1 for all subarrays of an odd length.

解题方法： 莫队算法。