codeforces 617E E. XOR and Favorite Number(莫队算法)

题目链接：

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

input

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

output

7
0

input

output

9
4
4

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n个数,有m个询问,问[l,r]之间有多少对i和j满足a[i]^a[i+1]^...^a[j]=k;

思路：暴力绝对绝对绝对是不行的,所有就要用复杂度更低的算法啦,所以我就去学了莫队算法,莫队算法处理的是一种离线算法,是对询问进行分块排序来优化查询的算法;

这题还要对异或运算要了解;我要去写个位运算的小总结;

AC代码：

#include <bits/stdc++.h>
using namespace std;
const int N=1e6+4;
struct node
{
    friend bool operator< (node x,node y)
    {
        if(x.pos==y.pos)return x.r<y.r;
        return x.l<y.l;
    }
    int l,r,id;
    int pos;
};
node qu[N];
int n,m,k;
int b[N],num[2*N];
long long ans[N];
void solve()
{
    memset(num,0,sizeof(num));
    int le=1,ri=0;
    long long temp=0;
    for(int i=1;i<=m;i++)
    {
        while(ri<qu[i].r)
        {
            ri++;
            temp+=num[b[ri]^k];//num[]数组是当前le到ri内每个b[i](le<=i<=ri)异或一个要添加的数==k的数目;所以num[b[ri]^k]就是在已有的区间上再加一个
            num[b[ri]]++;//ri前能和ri异或==k的数目;后面这些操作一样
        }
        while(ri>qu[i].r)
        {
            num[b[ri]]--;
            temp-=num[b[ri]^k];
            ri--;
        }
        while(le>qu[i].l-1)
        {
            le--;
            temp+=num[b[le]^k];
            num[b[le]]++;
        }
        while(le<qu[i].l-1)
        {
            num[b[le]]--;
            temp-=num[b[le]^k];
            le++;
        }
        ans[qu[i].id]=temp;
    }
}
int main()
{
    b[0]=0;
    scanf("%d%d%d",&n,&m,&k);
    for(int i=1;i<=n;i++)
    {
        scanf("%d",&b[i]);
        b[i]^=b[i-1];
    }
    int s=sqrt(n);
    for(int i=1;i<=m;i++)
    {
        scanf("%d%d",&qu[i].l,&qu[i].r);
        qu[i].id=i;
        qu[i].pos=qu[i].l/s;
    }
    sort(qu+1,qu+m+1);
    solve();
    for(int i=1;i<=m;i++)
    {
        cout<<ans[i]<<"
";
    }
    return 0;
}

codeforces 617E E. XOR and Favorite Number(莫队算法)

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