// C++ program for a Trie based O(n) solution to find max
// subarray XOR
#include<bits/stdc++.h>
using namespace std;
// Assumed int size
#define INT_SIZE 32
int k;
// A Trie Node
struct TrieNode
{
int value, ind; // Only used in leaf nodes
TrieNode *arr[2];
};
TrieNode *newNode()
{
TrieNode *temp = new TrieNode;
temp->value = 0;
temp->ind = -1;
temp->arr[0] = temp->arr[1] = NULL;
return temp;
}
void insert(TrieNode *root, int pre_xor, int id)
{
TrieNode *temp = root;
for (int i=INT_SIZE-1; i>=0; i--)
{
bool val = pre_xor & (1<<i);
if (temp->arr[val] == NULL)
temp->arr[val] = newNode();
temp = temp->arr[val];
}
temp->ind = id;
temp->value = pre_xor;
}
int query(TrieNode *root, int pre_xor, int r)
{
TrieNode *temp = root;
int mx = 0;
for (int i=INT_SIZE-1; i>=0; i--)
{
bool val = pre_xor & (1<<i);
if (temp->arr[1-val]!=NULL)
temp = temp->arr[1-val];
else if (temp->arr[val] != NULL)
temp = temp->arr[val];
if((temp->ind) > -1 && (pre_xor^(temp->value)) >= k)mx = max(mx, r-(temp->ind));
//~ cout << r << " " << temp->value << "\n";
//~ cout << temp->ind << " " << r << " " << temp->value << " " << pre_xor << " " << (pre_xor^(temp->value)) << " " << r-(temp->ind)+1 << "\n";
}
//~ cout << temp->ind << " " << r << " " << temp->value << " " << pre_xor << " " << (pre_xor^(temp->value)) << " " << "\n";
return mx;
}
// Returns maximum XOR value of a subarray in arr[0..n-1]
pair<int,int> maxSubarrayXOR(vector<int> arr, int n)
{
// Create a Trie and insert 0 into it
TrieNode *root = newNode();
insert(root, 0, -1);
int result = INT_MIN, pre_xor =0;
int ind = 0;
for (int i=0; i<n; i++)
{
pre_xor = pre_xor^arr[i];
insert(root, pre_xor, i);
if(query(root, pre_xor, i) > result){
result = query(root, pre_xor, i);
ind = i - result + 2;
}
}
return {ind,result};
}
// Driver program to test above functions
int main()
{
int n;
cin >> n >> k;
vector<int>arr(n);
for(int i = 0;i<n;i++)cin >> arr[i];
pair<int,int> p = maxSubarrayXOR(arr, n);
cout << p.first << " " << p.second << "\n";
return 0;
}
