// Author: Muhammed Khaled Shoeib
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
using namespace std;
//....................................................
// struct to speed-up the unordered data structures like map/set.
struct hash_function // unordered + modified hash >> ordered
{ static uint64_t splitmix64(uint64_t x) {
x += 0x9e3779b97f4a7c15; x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb; return x ^ (x >> 31); }
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM); } };
//....................................................
template < typename T, typename Compare = less < T > > // O(logn)
using ordered_set = tree < T, null_type, Compare, rb_tree_tag, tree_order_statistics_node_update>;
// less_equal: asc. not_unique, st.order_of_key(k) --> no. of items < k, less: unique
// greater_equal: desc. not_unique, st.order_of_key(k) --> no. of items > k, greater: unique
// *st.find_by_order(k) --> st[k] (Zero-indexed)
// less_equal (u can't erase here!) == multi-set
template < typename T > using maxpq = priority_queue < T >;
template < typename T > using minpq = priority_queue < T, vector< T >, greater< T > >;
//....................................................
#define boost ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
#define precision(a) cout << fixed << setprecision(a)
#define alo cout << "alooooooooooo!" << endl
#define YES cout << "YES" << endl
#define Yes cout << "Yes" << endl
#define yes cout << "yes" << endl
#define NO cout << "NO" << endl
#define No cout << "No" << endl
#define no cout << "no" << endl
#define ne cout << -1 << endl
#define endl "\n"
#define mem(mat, val) memset(mat, val, sizeof(mat))
#define ones(x) __builtin_popcountll(x)
#define msb(x) 63ll - __builtin_clzll(x)
#define lsb(x) __builtin_ffsll(x) - 1ll
//....................................................
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(),x.rend()
#define ceil_(a, b) (((ll)(a) + (ll)(b - 1)) / (ll)(b)) // up
#define floor_(a, b) (a / b) // down
#define round_(a, b) ((a + (b / 2ll)) / b) // nearest
//....................................................
// using ll = int; // take care of this shit!
using ll = long long;
using i64 = long long; using i32 = int;
using ld = long double; using ull = unsigned long long; using lli = long long int;
//......................................................
ll gcd_(ll x, ll y) { return y ? gcd_(y, x % y) : x; } // O(log(min(x, y)))
ll lcm_(ll a, ll b) { ll g = gcd_(a, b); return (a * b) / g; }
//mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
//#define getrand(l, r) uniform_int_distribution<long long>(l, r)(rng)
//......................................................
int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, 1, 0, -1};
int dx_diag[4] = { 1, 1, -1, -1 }, dy_diag[4] = { 1, -1, -1, 1 };
int dx_all[8] = {-1, -1, -1, 0, 1, 1, 1, 0}, dy_all[8] = {-1, 0, 1, 1, 1, 0, -1, -1};
int dx_knight[8] = {2, 2, 1, 1, -2, -2, -1, -1}, dy_knight[8] = {1, -1, 2, -2, 1, -1, 2, -2};
const ld pi = 3.141592653589793238462643383279; // acos(-1)
const ld eps = 1e-9;
const ll inf = (ll)INT32_MAX; // 2e9
const ll oo = (ll)1e15; // 1e15 (may cause OF in DP, Binary Search, ...)
const ll OO = (ll)INT64_MAX; // 9e18
const ll mod = (ll)1e9 + 7; // 1e9 + 7, 998244353
//..................................................... // string(len, char);
/*
* think twice, code once.
* think of different approaches to tackle a problem, write them down.
* think of different views of the problem, don't look from only one side.
* don't get stuck in one approach/problem.
* common mistakes: line 48, overflow (sum of many numbers), corner cases, over/under count, infinite loops,
* TLE, MLE (int instead of ll, using memset, Recursive DP, ...), RTE (out of bounds indexing), ....
*/
///____________________________________________ Shoeib __________________________________________________________
/* Binary Trie */
// usefull when dealing with a lot of binary numbers (we can move over all numbers in the same time).
// efficient insertion, deletion, counting, search for specific property (<, >, =, min, max, xor, ...), ...
// start from msb -to-> lsb.
// the time complexity of all operations is O(n), where n is the number of bits in the number being processed.
// if MLE --> remove useless variables.
// try to draw on a paper, and see information stored in each node.
// ....................
const ll mx_sz = 2, Bits = 30;
// ....................
struct Binary_Trie
{
struct Node
{
Node *ch[mx_sz];
ll freq, idx;
Node() { mem(ch, 0); freq = 0; idx = oo; }
};
Node *root;
Binary_Trie() { root = new Node(); }
void insert(const ll &x, const ll &i) // insert a new number
{
Node *curr = root;
for(ll bit = Bits; bit >= 0; bit--)
{
ll idx = ((x >> bit) & 1ll);
if(!curr->ch[idx]) curr->ch[idx] = new Node();
curr = curr->ch[idx];
curr->freq++;
curr->idx = min(curr->idx, i);
}
}
// more methods ...
ll query(const ll &x, const ll &k) // return min index, have xor >= k
{
Node *curr = root;
ll ret = 2*oo;
for(ll bit = Bits; bit >= 0; bit--)
{
if(((x >> bit) & 1ll)) // 1
{
if(((k >> bit) & 1ll)) // 1
{
// can't take ones, go to zeros
if(curr->ch[0])
{
if(bit == 0) ret = min(ret, curr->ch[0]->idx);
curr = curr->ch[0];
}
else return ret;
}
else // 0
{
// take all zeros, go to ones
if(curr->ch[0]) ret = min(ret, curr->ch[0]->idx);
if(curr->ch[1])
{
if(bit == 0) ret = min(ret, curr->ch[1]->idx);
curr = curr->ch[1];
}
else return ret;
}
}
else // 0
{
if(((k >> bit) & 1ll)) // 1
{
// can't take zeros, go to ones
if(curr->ch[1])
{
if(bit == 0) ret = min(ret, curr->ch[1]->idx);
curr = curr->ch[1];
}
else return ret;
}
else // 0
{
// take all ones, go to zeros
if(curr->ch[1]) ret = min(ret, curr->ch[1]->idx);
if(curr->ch[0])
{
if(bit == 0) ret = min(ret, curr->ch[0]->idx);
curr = curr->ch[0];
}
else return ret;
}
}
}
return ret;
}
};
// ....................
void solve()
{
ll n, k; cin >> n >> k;
vector < ll > a(n + 1); a[0] = 0;
for(ll i = 1; i <= n; i++) cin >> a[i];
Binary_Trie trie = Binary_Trie();
ll xor_sm = 0, l = 0, len = 0;
for(ll i = 0; i <= n; i++)
{
xor_sm ^= a[i];
ll ret = trie.query(xor_sm, k);
if(ret != oo)
{
ret++;
if(i - ret + 1 > len)
{
l = ret;
len = i - ret + 1;
}
}
trie.insert(xor_sm, i);
}
cout << l << ' ' << len << endl;
return;
}
signed main()
{
boost;
// freopen("assessment.in", "r", stdin);
// freopen("output.txt", "w", stdout);
// precision(15);
i32 _ = 1; //cin >> _;
// cout.flush();
while(_--) solve();
return 0;
}
