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 \le i \le j \le r and the xor of the numbers ai,ai+1,...,aj is equal to k.
The first line of the input contains integers n, m and k (1 \le n,m \le 100000, 0 \le k \le 1000000)- the length of the array, the number of queries and Bob's favorite number respectively.
The second line contains n integers ai (0 \le ai \le 1000000)- Bob's array.
Then m lines follow. The i-th line contains integers li and ri (1 \le li \le ri \le n)- the parameters of the i-th query.
Print m lines, answer the queries in the order they appear in the input.
6 2 3 1 2 1 1 0 3 1 6 3 5· · \n · · · · · \n · \n · \n
7 0\n \n
5 3 1 1 1 1 1 1 1 5 2 4 1 3· · \n · · · · \n · \n · \n · \n
9 4 4\n \n \n
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.