主题

主题

 
   

E. XOR and Favorite Number

原题:http://codeforces.com/problemset/problem/617/E

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.


题目大意:

给出一个长度为n的序列与一个非负整数k,给出m次询问:

  1. 查询区间[li..ri]有多少段子区间异或和为k


个人解法:

作为E题恐怕还是水了一点?也许在当年不算水吧。

我们上莫队,维护桶。转移的时候考虑一下贡献就可以了。


代码如下:

http://codeforces.com/contest/617/submission/25978412

 
 
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