## FREQ2 - Most Frequent Value

You are given a sequence of n integers a0, a1 ... an-1. You are also given several queries consisting of indices i and j (0 ≤ i ≤ j ≤ n-1). For each query, determine the number of occurrences of the most frequent value among the integers ai ... aj.

### Input

First line contains two integers n and q (1 ≤ n, q ≤ 100000). The next line contains n integers a0 ... an-1 (0 ≤ ai ≤ 100000, for each i ∈ {0 ... n-1}) separated by spaces. The following q lines contain one query each, consisting of two integers i and j (0 ≤ i ≤ j ≤ n-1), which indicates the boundary indices for the query.

### Output

For each query, print one line with one integer: The number of occurrences of the most frequent value within the given range.

### Example

```Input:5 31 2 1 3 30 21 20 4

Output:
212```

## Code Examples

### #1 Code Example with C++ Programming

```Code - C++ Programming```

``````#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

#define MOD                 1000000007LL
#define EPS                 1e-9
#define io                  ios_base::sync_with_stdio(false);cin.tie(NULL);

const int N = 1e5+5;
const int M = 1e5+5;
const int SQN = sqrt(N) + 1;

struct query{
int l, r;
int idx;
int block;
query(){}
query(int _l, int _r, int _id){
l = _l;
r = _r;
block = _l/SQN;
idx = _id;
}
bool operator < (const query &b) const{
if(block != b.block)
return block < b.block;
return r < b.r;
}

};

query Q[M];
int ans[M];
int n, q;
int arr[N];
int freq[N], counter[N];

int main(){
scanf("%d%d", &n, &q);
for(int i = 1;i <= n; i++)
scanf("%d", arr+i);
for(int i = 1;i <= q; i++){
int l, r;
scanf("%d%d", &l, &r);
l++;r++;
Q[i] = query(l, r, i);
}
sort(Q+1, Q+1+q);
int curl = 1, curr = 0;
int t_ans = 0;
for(int i = 1;i <= q; i++){
int l = Q[i].l;
int r = Q[i].r;
int idx = Q[i].idx;
while(curr < r){
++curr;
int val = arr[curr];
int c = freq[val];
counter[c]--;
freq[val]++;
counter[freq[val]]++;
t_ans = max(t_ans, freq[val]>;
}
while(curl > l){
--curl;
int val = arr[curl];
int c = freq[val];
counter[c]--;
freq[val]++;
counter[freq[val]]++;
t_ans = max(t_ans, freq[val]);
}
while(curr > r){
int val = arr[curr];
int c = freq[val];
counter[c]--;
freq[val]--;
counter[freq[val]]++;
while(counter[t_ans] == 0)	t_ans--;
--curr;
}
while(curl < l){
int val = arr[curl];
counter[freq[val]]--;
freq[val]--;
counter[freq[val]]++;
while(counter[t_ans] == 0)	t_ans--;
++curl;
}
ans[idx] = t_ans;
}
for(int i = 1;i <= q; i++){
printf("%d\n", ans[i]);
}
return 0;
}``````
Copy The Code &

Input

cmd
5 3
1 2 1 3 3
0 2
1 2
0 4

Output

cmd
2
1
2