XOR

Consider an array A with n elements. Each of its element is A[i] (1 ≤ i ≤ n). Then gives two integers
Q, K, and Q queries follow. Each query, give you L, R, you can get Z by the following rules.
 To get Z, at first you need to choose  some elements from A[L] to A[R], we call them A[i1], A[i2],
. . . , A[it], Then you can get number Z = K or (A[i1], A[i2], . . . , A[it]).
   Please calculate the maximum Z for each query .

Input
Several test cases.
First line an integer T (1 ≤ T ≤ 10). Indicates the number of test cases.
Then T  test cases follows. Each test case begins with three integer N, Q, K (1 ≤ N ≤ 10000,1 ≤
Q ≤ 100000, 0 ≤ K ≤ 100000). The next line has N integers indicate A[1] to A[N] (0 ≤ A[i] ≤ 108).
Then Q lines, each line two integer L, R (1 ≤ L ≤ R ≤ N).

Output
For each query, print the answer in a single line.

Sample Input
1
5 3 0
1 2 3 4 5
1 3
2 4
3 5

Sample Output
3
7
7

題意：t組資料，然後輸入n，k，q，接著給出一個1個長度為n的陣列,q個詢問，對於每個詢問，詢問在下標為[l,r]的數中，選取一部分數，使得其異或值再OR上k後最大，輸出這個最大值。

思路：根據題意，選取一部分值得到異或最大值，可以想到線性基，但是最後要OR上k，所以要消除k對其影響，我們就把每個數轉化成二進位制，然後將k為1的位置對於每個數其位置就變為0，這樣就可以消除其k的影響了，最後在OR上k變回來，即為正確答案。比如數a[i]=6(110) ,k = 4(100),則a[i]應該變為(010)=2這樣來消除k的影響。由於多次區間詢問，所以用線段樹維護一下即可。

AC程式碼：

#include<cstdio>
#include<cmath>
#include<cstring>
#include<string>
#include<cstdlib>
#include<algorithm>
#include<iostream>
#include<queue>
#include<stack>
#include<map>

using namespace std;

#define FOU(i,x,y) for(int i=x;i<=y;i++)
#define FOD(i,x,y) for(int i=x;i>=y;i--)
#define MEM(a,val) memset(a,val,sizeof(a))
#define PI acos(-1.0)

const double EXP = 1e-9;
typedef long long ll;
typedef unsigned long long ull;
const int INF = 0x3f3f3f3f;
const ll MINF = 0x3f3f3f3f3f3f3f3f;
const double DINF = 0xffffffffffff;
const int mod = 1e9+7;
const int N = 1e4+5;


//線性基
struct L_B{
    ll d[63],new_d[63];  //d陣列是第一次線性基,new_d是用於求Kth的線性基
    int cnt;             //記錄個數
    L_B(){
        memset(d,0,sizeof(d));
        memset(new_d,0,sizeof(new_d));
        cnt=0;
}
void clear(){
    memset(d,0,sizeof(d));
    memset(new_d,0,sizeof(new_d));
    cnt=0;
}
    bool ins(ll val){
        for(int i=62;i>=0;i--){
            if(val&(1ll<<i)){  //存在貢獻則繼續
                if(!d[i]){     //線性基不存在,選入線性基中
                    d[i]=val;
                    break;
                }
                val^=d[i];     //否則直接改變其值
            }
        }
        return val>0;          //大於0則是成功加入線性基的向量
    }
    ll query_max(){
        ll ans=0;
        for(int i=62;i>=0;i--)
            if((ans^d[i])>ans) //能讓值變大則選入
                ans^=d[i];
        return ans;
    }
    ll query_min(){
        for(int i=0;i<=62;i++)
            if(d[i])           //最小異或值
                return d[i];
        return 0;
    }
    //以下程式碼為求第k大異或值，其中cnt用於判斷是否可以取到0
    // cnt==n（數的個數）則不可以取到0，第k小就是第k小，否則第k小是第k-1小
    void rebuild()
    {
        for(int i=62;i>=0;i--)
            for(int j=i-1;j>=0;j--)
                if (d[i]&(1LL<<j))
                    d[i]^=d[j];
        for (int i=0;i<=62;i++)
            if (d[i])
                new_d[cnt++]=d[i];
    }
    ll kthquery(int k)
    {
        ll ans=0;
        if (k>=(1ll<<cnt))
            return -1;
        for (int i=62;i>=0;i--)
            if (k&(1ll<<i))
                ans^=new_d[i];
        return ans;
    }
};

//線性基合併,暴力合併
L_B merge(const L_B &n1,const L_B &n2)
{
    L_B ret=n1;
    for (int i=62;i>=0;i--)
        if (n2.d[i])
            ret.ins(n2.d[i]);
    return ret;
}

ll n,q,k,pd,a[N];
L_B A;

struct node{
    int lft,rht;
    L_B lb;
}tree[N<<2];

void pushUp(int id){
    tree[id].lb = merge(tree[id<<1].lb,tree[id<<1|1].lb);
}

void build(int id,int l,int r){
    tree[id].lft=l;
    tree[id].rht=r;
    if(l==r){
        tree[id].lb.clear();
        tree[id].lb.ins((a[l]&pd));
        return ;
    }
    int mid = (l+r)>>1;
    build(id<<1,l,mid);
    build(id<<1|1,mid+1,r);
    pushUp(id);
}

void query(int id,int l,int r){
    if(l==tree[id].lft&&r==tree[id].rht){
        A = merge(A,tree[id].lb);
        return ;
    }
    int mid = (tree[id].lft+tree[id].rht)>>1;
    if(r<=mid){
        query(id<<1,l,r);
    }
    else if(l>mid){
        query(id<<1|1,l,r);
    }
    else{
        query(id<<1,l,mid);
        query(id<<1|1,mid+1,r);
    }
}

int main()
{
    std::ios::sync_with_stdio(false);
    int t;
    scanf("%d",&t);
    while(t--){
        scanf("%lld%lld%lld",&n,&q,&k);
        for(int i=1;i<=n;i++)
            scanf("%lld",&a[i]);
        pd=0;
        for(int i=0;i<=62;i++){
            if(k&(1ll<<i))
                ;
            else
                pd+=(1ll<<i);
        }
        build(1,1,n);
        int l,r;
        while(q--){
            scanf("%d%d",&l,&r);
            A.clear();
            query(1,l,r);
            printf("%lld\n",A.query_max()|k);
        }
    }
    return 0;
}