// Success consists of going from failure to failure without loss of enthusiasm
#include <bits/stdc++.h>
using namespace std;
#define nl '\n'
const int INF = 1e9+10;
const int BITS = 30;
int C = 0;
struct Trie {
int smallest_index, ID; // smallest index of a value in this sub-trie
Trie* children[2]; // (either 0 or 1)
Trie(int x) { smallest_index = INF, ID = x; children[0] = children[1] = NULL; }
void insert_value(int value, int index, int bit = BITS) {
// inserts x into the trie
smallest_index = min(smallest_index, index); // update smallest index in sub-trie
if (bit == -1) return;
int value_bit = (value >> bit) & 1;
if (!children[value_bit]) children[value_bit] = new Trie(C++); // create node if needed
children[value_bit]->insert_value(value, index, bit - 1); // recurse from child node
}
int find_smallest_index(int x, int y, int bit = BITS) {
// returns smallest index such that P xor x >= y, where P is a element in the trie
if (bit == -1) return INF;
int current_answer = INF;
int x_bit = (x >> bit) & 1, y_bit = (y >> bit) & 1; // get b-th bits of x and y
int p_bit = x_bit ^ 1; // want to maximize P xor x hence want to have opposite bits (if possible)
if (!children[p_bit]) p_bit ^= 1; // not possible (must go to other option)
if ((x_bit ^ p_bit) < y_bit) {
return INF; // cannot have (P xor x) < y at any level
}
if ((x_bit ^ p_bit) > y_bit) {
// already have P xor x > y, hence all other bits don't matter
// cout << x << " + " << y << " + " << bit << endl;
// cout << x_bit << " - " << y_bit << " - " << p_bit << endl;
// cout << "ANS: " << children[p_bit]->smallest_index << endl;
current_answer = min(current_answer, children[p_bit]->smallest_index);
// take smallest index in the sub-trie
p_bit ^= 1; // continue down other possibility
}
if (!children[p_bit]) return current_answer; // cannot go further down
if (bit == 0) { // reached equality
current_answer = min(current_answer, children[p_bit]->smallest_index); // take possible answer
// cout << "ANS: " << children[p_bit]->smallest_index << endl;
}
current_answer = min(current_answer, children[p_bit]->find_smallest_index(x, y, bit - 1));
return current_answer;
}
};
int main() {
cin.tie(0)->sync_with_stdio(0);
int N, X; cin >> N >> X;
vector<int> seq(N); for(auto& x : seq) cin >> x;
Trie trie(C++);
int current_xor = 0; trie.insert_value(current_xor, -1);
int answer = 0, best_index = -1;
for(int index = 0; index < N; index++) {
current_xor ^= seq[index];
int position = trie.find_smallest_index(current_xor, X); // get best position
if (answer < (index - position)) { // check if its a better answer
answer = (index - position);
best_index = position + 1; // position is exclusive
}
trie.insert_value(current_xor, index);
}
cout << best_index + 1 << " " << answer << nl;
return 0;
}
