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. 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. Print m lines, answer the queries in the order they appear in the input. 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.