Lets rephrase the problem a little bit. Denote by P[i] the XOR of numbers a[1], a[2], ..., a[i]. Now the XOR of subarray [L, R] becomes P[R] XOR P[L — 1] and the problem boils down to finding how many pairs of numbers from a list, when XOR-ed give a number less than K. This problem can be solved in O(NlogN) with the help of the Walsh-Hadamard transform and you can get some insight for the implementation from here: https://csacademy.com/blog/fast-fourier-transform-and-variations-of-it