F. Tree and XORtime limit per test4 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a connected undirected graph without cycles (that is, a tree) of n vertices, moreover, there is a non-negative integer written on every edge.Consider all pairs of vertices (v, u) (that is, there are exactly n^2 such pairs) and for each pair calculate the bitwise exclusive or (xor) of all integers on edges of the simple path between v and u. If the path consists of one vertex only, then xor of all integers on edges of this path is equal to 0.Suppose we sorted the resulting n^2 values in non-decreasing order. You need to find the k-th of them.The definition of xor is as follows.Given two integers x and y, consider their binary representations (possibly with leading zeros): x_k \dots x_2 x_1 x_0 and y_k \dots y_2 y_1 y_0 (where k is any number so that all bits of x and y can be represented). Here, x_i is the i-th bit of the number x and y_i is the i-th bit of the number y. Let r = x \oplus y be the result of the xor operation of x and y. Then r is defined as r_k \dots r_2 r_1 r_0 where: r_i = \left\{ \begin{aligned} 1, ~ \text{if} ~ x_i \ne y_i \\ 0, ~ \text{if} ~ x_i = y_i \end{aligned} \right. InputThe first line contains two integers n and k (2 \le n \le 10^6, 1 \le k \le n^2) — the number of vertices in the tree and the number of path in the list with non-decreasing order.Each of the following n - 1 lines contains two integers p_i and w_i (1 \le p_i \le i, 0 \le w_i < 2^{62}) — the ancestor of vertex i + 1 and the weight of the corresponding edge.OutputPrint one integer: k-th smallest xor of a path in the tree.ExamplesInput2 11 3Output0Input3 61 21 3Output2NoteThe tree in the second sample test looks like this:For such a tree in total 9 paths exist:   1 \to 1 of value 0  2 \to 2 of value 0  3 \to 3 of value 0  2 \to 3 (goes through 1) of value 1 = 2 \oplus 3  3 \to 2 (goes through 1) of value 1 = 2 \oplus 3  1 \to 2 of value 2  2 \to 1 of value 2  1 \to 3 of value 3  3 \to 1 of value 3 
Input2 11 3
Output0
['strings', 'trees', '*2900']