#include <bits/stdc++.h>
// #include "atcoder/convolution.hpp"
// #include "atcoder/dsu.hpp"
// #include "atcoder/fenwicktree.hpp"
// #include "atcoder/lazysegtree.hpp"
// #include "atcoder/math.hpp"
// #include "atcoder/maxflow.hpp"
// #include "atcoder/mincostflow.hpp"
// #include "atcoder/modint.hpp"
// #include "atcoder/scc.hpp"
// #include "atcoder/segtree.hpp"
// #include "atcoder/string.hpp"
// #include "atcoder/twosat.hpp"
using namespace std;
//using namespace atcoder;
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#define ll long long
#define pb push_back
#define F first
#define S second
#define I insert
#define ull unsigned long long
typedef long double lld;
#define PI 3.141592653589793238462
#define set_bits __builtin_popcountll
#define mem(x,v) memset(x,v,sizeof(x))
#define inp(v,n) loo(i,n){cin>>v[i];}
#ifndef ONLINE_JUDGE
#define debug(x) cerr << #x <<" "; _print(x); cerr << endl;
#else
#define debug(x)
#endif
void _print(ll t) {cerr << t;}
void _print(int t) {cerr << t;}
void _print(string t) {cerr << t;}
void _print(char t) {cerr << t;}
void _print(lld t) {cerr << t;}
void _print(double t) {cerr << t;}
void _print(ull t) {cerr << t;}
template <class T, class V> void _print(pair <T, V> p);
template <class T> void _print(vector <T> v);
template <class T> void _print(set <T> v);
template <class T, class V> void _print(map <T, V> v);
template <class T> void _print(multiset <T> v);
template <class T, class V> void _print(pair <T, V> p) {cerr << "{"; _print(p.F); cerr << ","; _print(p.S); cerr << "}";cerr<<"\n";}
template <class T> void _print(vector <T> v) {cerr << "[ "; for (T i : v) {_print(i); cerr << " ";} cerr << "]";cerr<<"\n";}
template <class T> void _print(set <T> v) {cerr << "[ "; for (T i : v) {_print(i); cerr << " ";} cerr << "]";cerr<<"\n";}
template <class T> void _print(multiset <T> v) {cerr << "[ "; for (T i : v) {_print(i); cerr << " ";} cerr << "]";cerr<<"\n";}
template <class T, class V> void _print(map <T, V> v) {cerr << "[ "; for (auto i : v) {cerr<<"{"<<i.F<<" "<<i.S<<"} ";} cerr << "]";cerr<<"\n";}
#define vll vector<ll>
#define vdd vector<double>
#define vss vector<string>
#define vpl vector<pair<ll,ll>>
#define vcl vector<char>
#define vvl vector<vector<ll>>
#define vvc vector<vector<char>>
#define ppi pair<ll,ll>
#define maxe(v) *max_element((v).begin(),(v).end());
#define mine(v) *min_element((v).begin(),(v).end());
#define loo(i,n) for(long long i=0;i<n;i++)
#define sor(v) sort(v.begin(),v.end());
#define pyes cout<<"YES\n";
#define pno cout<<"NO\n";
#define ayes cout<<"Yes\n";
#define ano cout<<"No\n";
#define mll map<ll,ll>
#define mcl map<char,ll>
#define mod 1000000007
#define ft front()
#define bk back()
#define pf push_front
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend()
#define lb lower_bound
#define ub upper_bound
#define each(a,x) for(auto a:x)
#define nl cout<<"\n";
#define pri(xx) cout<<xx<<"\n";
#define sll set<ll>
#define sch set<char>
#define rt return
#define sz(x) x.size()
#define pq priority_queue
#define pql priority_queue<ll>
#define INF 1e9
#define manh(a,b,c,d) abs(a-c)+abs(b-d)
#define euc(a,b,c,d) sqrt((a-c)*(a-c)+(b-d)*(b-d))
#define foo(i,a,b) for(ll i=a;i<b;i++)
#define pril(i,a,b,v) foo(i,a,b){cout<<v[i]<<" ";}
#define pqc priority_queue<char>
#define to_upper(s) transform(s.begin(), s.end(), s.begin(), ::toupper);
#define lowercase(s) transform(s.begin(), s.end(), s.begin(), ::tolower);
vvl prefx2(vvl &v){
ll n=v.size(),m=v[0].size();
vvl pre=v;
loo(i,n){
loo(j,m){
pre[i][j]+=((i-1>=0 ? pre[i-1][j] : 0)+(j-1>=0 ? pre[i][j-1] : 0)-((i-1>=0 and j-1>=0) ? pre[i-1][j-1] : 0));
}
}
return pre;
}
ll preQ2(ll x,ll y,ll a,ll b,vvl &pre){
return pre[a][b]-((x-1>=0) ? pre[x-1][b] : 0)-((y-1>=0)? pre[a][y-1] : 0)+((x-1>=0 and y-1>=0) ? pre[x-1][y-1] : 0);
}
vll prefx(vll &v){
vll pre=v;
loo(i,pre.size()) pre[i]+=(i-1>=0 ? pre[i-1] : 0);
return pre;
}
ll preQ1(ll l,ll r,vll &pre){
return (pre[r]-(l-1>=0 ? pre[l-1] : 0));
}
/* //SNIPPET LIST
// 1)segtree
-(used to build a segment tree and to solve range based queries and point update)
2)freqidblocks
-(in a vector we can find number of increasing and decreasing subsegment)
3)UNIV -(gives unique vector no duplicates)
4)levaltraversalTree
5)bpow
6)sttoi
7)commonsubstring2chr
8)factorstore-(stores all the factors of a num)
9)issubstring
10)perfectSqorNot
11)seivestore
12)precompfac -(factorial)
13)range overlap
14)countfreqcontinuos -(ex--> v=(1,1,1,2) return vpl={{1,3},{2,1}})
15)getMaxContifreq -(same as above but gives maximum of all same number)
(ex---> v=(1,1,2,1,1,1) return freq freq[1]=3 & freq[2]=1 and all other 0)
16)DSU*snipp ------->(Contains all functions of dsu like unite, find par) (***imp***)
17)lpf for lowest prime factor snippet lps[i]--->lowest prime factor of i
18)LPS of a string ---->Longest proper sufix which is also a prefix, return a vector of that lenth for every char
19)KMP algo-------->takes string s,p as attr and gives starting occurences of p in s as vector
20)zFunction--------->Gives Z array of a string (starting from index i how much is equal to prefix type question)
21)Range Update Point query Push down type query (RUPU_PUSHDOWN)-------->Used to give answer range update questions no lazy and after updating a node in segment tree we need to Propagate the result to lower nodes
(Knight tournament in cf best example)
22) kth Segment tree ---> Its simply ordered set implementation via segment trees and used for questions of type Queue Construction in leetcode
23) **********STACK RELATED ALL SNIPPETS************
1)NGER--->Next greater elemnt to right for every elemnt in array
2)NGEL--->Next greater elemnt to left for every elemnt in array
3)NLEL--->Next leeser elemnt to right for every elemnt in array
4)NLER---->Next lesser element to left for every elemnt in array and also gives position of that least elemnt (this one only returns vpl).
5)
24) Trie implementation--> Gives a template for string trie problems
25) LinearDioEquation ----->Gives Linear DIophantine equation Snippet (ex: ax+by=c if c%gcd(a,b)==0 then there exists a solution which can be found and using this one solution we find all other solutions)
26) EulerTotientFunction-------> Gives no of integers that are relatively prime with n in log(n)
phi(n). ex phi(10)=4 (2,3,7,9).
27) RabinMillerTest to find Primes less than 1o^18 in log(n) complexity
(HERE MULTIPLICATION is in o(1)) and also checks prime or not in log(n)
28) LcmOfArray-----> Gives the lcm of the array using primes fact method o(nlogn)
29) Check_N_as_Sum_Of_Two_Squares----> can check whether a given n can be expressed as sum of squares
i.e n=a^2+b^2 on O(1) (precomputation)
30) manacherAlgo ---> to get longest palindrom or s[l..r] is pal or not
31) contrbAsMaxMin --->for every element in array we can calculate its contrib as max / min in a subarray
32) SumOfNumberOfDistNumOfAllSubarrays ----> gives summ(number of distinct numbers in all subarrays) ex:(1,1,2) -->[(1),(1),(2),(1,2),(1,1),(1,1,2)] 1+1+1+2+1+2=7
33) custom_comparator ---> Comparator function for priority queues
34) LisEndingAt ----> takes an array and returns dp array giving max lis length at that point (via segment tree compression)
(*******Also can be used to know max lis achieve if we start at a point********)
35) k_sizeWindowRollingMedian snippet -----> used to find ,edian of every k sized subbarray in an array using two multisets(very very good model)
36) Serial bit operations snippet where you can find (or xor and in log(n)) for a range l to r
37) LucasTheorem ----> gives (ncr) modulo p , p is prime
TC: O(plogn basep)
38) BinaryLiftingLCA ---> Give LCA (u,v) in LOGN
39) PathAggregates1 ---> Given node values instead of edge weights then you can get path_op(u,v)
40) PathAgrregates2 ---> Given edge wieights then use pushdown method
*/
vpl movmt1={{0,1},{1,0},{-1,0},{0,-1}};
vpl movmt2={{0,1},{1,0},{-1,0},{0,-1},{1,-1},{-1,-1},{1,1},{-1,1}};
bool isvalid(ll x,ll y,ll n,ll m){
return (x>=0 and x<n and y>=0 and y<m);
}
// using mint1=modint1000000007;
// using mint2=modint998244353;
/*ll MAXN = 2000005;
vector<mint> fact(MAXN),inv_fact(MAXN);
void precompute_factorials() {
fact[0] = 1;
for (ll i = 1; i < MAXN; i++) {
fact[i] = fact[i - 1] * i;
}
inv_fact[MAXN - 1] = fact[MAXN - 1].inv(); // Use modll's inv() for modular inverse
for (ll i = MAXN - 2; i >= 0; i--) {
inv_fact[i] = inv_fact[i + 1] * (i + 1);
}
}
mint nCr(ll n, ll r) {
if (r > n || r < 0) return 0;
return fact[n] * inv_fact[r] * inv_fact[n - r];
}
mint nPr(ll n, ll r) {
if (r > n || r < 0) return 0;
return fact[n] * inv_fact[n - r];
}*/
// __builtin_popcount Count 1-bits (int)
// __builtin_popcountll Count 1-bits (long long)
// __builtin_clz Count leading zeros (int)
// __builtin_clzll Count leading zeros (long long)
// __builtin_ctz Count trailing zeros (int)
// __builtin_ctzll Count trailing zeros (long long)
// __builtin_parity Parity of bits (int)
// __builtin_parityll Parity of bits (long long)
// __builtin_ffs 1-based index of least significant 1
class Trie{
public:
Trie* child[2];
int mi;
Trie(){
child[0]=child[1]=NULL;
mi=1e9;
}
};
Trie* root=new Trie();
void insert(int x,int ind){
Trie* cur=root;
for(int i=20;i>=0;i--){
int b=(x>>i)&1;
if(cur->child[b]==NULL) cur->child[b]=new Trie();
cur=cur->child[b];
cur->mi=min(cur->mi,ind);
}
}
pair<int,int> query(int x,int k,int ind){
Trie* cur=root;
int ans=-1;
int st=-1;
for(int i=20;i>=0;i--){
if(!cur){
return {st,ans};
}
int kbit=(k>>i)&1;
int xbit=(x>>i)&1;
// we need xor to be >k => that specific bit is 1 prefered
if(kbit==0){
if(cur->child[1-xbit]){
// xor>k
int res=ind-cur->mi;
if(res>ans){
ans=res;
st=ind-ans+1;
return {st,ans};
}
}
cur=cur->child[xbit];
}
else{
cur=cur->child[1-xbit];
}
}
return {st,ans};
}
void madara(){
int n,k;
cin>>n>>k;
vector<int> v(n);
inp(v,n)
if(k==0){
cout<<1<<" "<<n<<endl;
rt;
}
ll p=0;
insert(0,0);
ll st=-1,ans=-1;
for(int i=1;i<=n;i++){
p^=v[i-1];
auto [ind,len]=query(p,k-1,i);
// cout<<ind<<" "<<len<<endl;
insert(v[i-1],i);
if(len>ans){
ans=len;
st=ind;
}
}
cout<<st<<" "<<ans<<endl;
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
#ifndef ONLINE_JUDGE
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
freopen("Error.txt", "w", stderr);
#endif
ll ashish;
ashish=1;
while(ashish--){
madara();
}
return 0;
}
/*
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*/
