Codeforces Round #340 (Div. 2)E. XOR and Favorite Number 莫队算法

E. XOR and Favorite Number

 

Bob has a favorite number k and ai of length n. Now he asks you to answer m queries. Each query is given by a pair li and ri and asks you to count the number of pairs of integers i and j, such that l ≤ i ≤ j ≤ r and the xor of the numbers ai, ai + 1, ..., aj is equal to k.

Input

The first line of the input contains integers n, m and k (1 ≤ n, m ≤ 100 000, 0 ≤ k ≤ 1 000 000) — the length of the array, the number of queries and Bob's favorite number respectively.

The second line contains n integers ai (0 ≤ ai ≤ 1 000 000) — Bob's array.

Then m lines follow. The i-th line contains integers li and ri (1 ≤ li ≤ ri ≤ n) — the parameters of the i-th query.

Output

Print m lines, answer the queries in the order they appear in the input.

Examples

6 2 3
1 2 1 1 0 3
1 6
3 5

7
0

Note

In the first sample the suitable pairs of i and j for the first query are: (1, 2), (1, 4), (1, 5), (2, 3), (3, 6), (5, 6), (6, 6). Not a single of these pairs is suitable for the second query.

In the second sample xor equals 1 for all subarrays of an odd length.

题意：

给你1~n的数，m次询问，每次问你l,r之间a[x]^a[y]=k的对数有多少

题解：

莫队离线做，

预处理异或前缀和，

每次按照莫队算法解除答案就好了

#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
using namespace std;
const int maxn = 120010, M = 1e5+10, mod = 1e9 + 7, inf = 0x3f3f3f3f;
typedef long long ll;

int pos[maxn],col[maxn],f[5000000],n,m,k;
ll Ans[maxn];
struct Query{
    int l,r,id;
    friend bool operator < (const Query &R,const Query &T){
        return pos[R.l]<pos[T.l] || (pos[R.l]==pos[T.l] && R.r<T.r);
    }
}Q[maxn];
void init(){
    scanf("%d%d%d",&n,&m,&k);
    for(int i=1;i<=n;++i)scanf("%d",&col[i]);
    for(int i=1;i<=n;i++) col[i]^=col[i-1];
    int limit=(int)sqrt((double)n+0.5);
    for(int i=1;i<=n;++i)pos[i]=(i-1)/limit+1;//左端点分块
    for(int i=1;i<=m;++i){
        scanf("%d%d",&Q[i].l,&Q[i].r);
        Q[i].id=i;
    }
    sort(Q+1,Q+m+1);
}
void modify(int p,ll &ans,int add){
    if(add>0) {
        ans=ans+add*f[col[p]^k];f[col[p]]+=add;
    }
    else {
         f[col[p]]+=add;ans=ans+add*f[col[p]^k];
    }
}
void solve(){
    ll ans=0;
    int l=1,r=0;
    f[0]=1;
    for(int i=1;i<=m;++i){
        int id=Q[i].id;
        while(r<Q[i].r) modify(++r,ans,1);
        while(l>Q[i].l) --l,modify(l-1,ans,1);
        while(r>Q[i].r) modify(r--,ans,-1);
        while(l<Q[i].l) modify(l-1,ans,-1),l++;
        Ans[id] = ans;
    }
    for(int i=1;i<=m;++i)
        printf("%I64d\n",Ans[i]);
}
int main(){
    init();
    solve();
    return 0;
}