B. Vladik and Complicated Book

Vladik had started reading a complicated book about algorithms containing n pages. To improve understanding of what is written, his friends advised him to read pages in some order given by permutationP = [p₁, p₂, ..., p_n], where p_i denotes the number of page that should be readi-th in turn.

Sometimes Vladik’s mom sorted some subsegment of permutation P from position l to positionr inclusive, because she loves the order. For every of such sorting Vladik knows numberx — what index of page in permutation he should read. He is wondered if the page, which he will read after sorting, has changed. In other words, hasp_x changed? After every sorting Vladik return permutation to initial state, so you can assume that each sorting is independent from each other.

Input

First line contains two space-separated integers n,m (1 ≤ n, m ≤ 10⁴) — length of permutation and number of times Vladik's mom sorted some subsegment of the book.

Second line contains n space-separated integersp₁, p₂, ..., p_n (1 ≤ p_i ≤ n) — permutationP. Note that elements in permutation are distinct.

Each of the next m lines contains three space-separated integersl_i,r_i,x_i (1 ≤ l_i ≤ x_i ≤ r_i ≤ n) — left and right borders of sorted subsegment in i-th sorting and position that is interesting to Vladik.

Output

For each mom’s sorting on it’s own line print "Yes", if page which is interesting to Vladik hasn't changed, or "No" otherwise.

Examples

Input

5 55 4 3 2 11 5 31 3 12 4 34 4 42 5 3

Output

YesNoYesYesNo

Input

6 51 4 3 2 5 62 4 31 6 24 5 41 3 32 6 3

Output

YesNoYesNoYes

Note

Explanation of first test case:

1. [1, 2, 3, 4, 5] — permutation after sorting, 3-rd element hasn’t changed, so answer is "Yes".
2. [3, 4, 5, 2, 1] — permutation after sorting, 1-st element has changed, so answer is "No".
3. [5, 2, 3, 4, 1] — permutation after sorting, 3-rd element hasn’t changed, so answer is "Yes".
4. [5, 4, 3, 2, 1] — permutation after sorting, 4-th element hasn’t changed, so answer is "Yes".
5. [5, 1, 2, 3, 4] — permutation after sorting, 3-rd element has changed, so answer is "No".

题意：第一行，书的页数，和书页变化的次数，给出一个书的顺序

给出变换的是这样变的：给出 变化的下标（第几页到第几页） left 和 right，还有一个变量p，这个区间从小到大排序，看看 第 p 个点，的值有没有变。  

如果 用的 sort 把区间排序，会超时。

//2.#if 0#include<bits/stdc++.h>using namespace std;int main(){int n,t,a[10000];while(cin>>n>>t){for(int i=1; i<=n; i++){cin>>a[i];}while(t--){int l,r,p;cin>>l>>r>>p;if(p<l&&p>r){cout<<"Yes"<<endl;}else{int c[10000]={0},d[10000]={0},num=0;for(int i=l; i<=r; i++) {if(a[i]<a[p])num++; }if(a[p]==a[l+num]) {cout<<"Yes"<<endl;}else{cout<<"No"<<endl;}//sort(c,c+(r-l+1));/*for(int i=0; i<l-1; i++){d[i]=a[i];}for(int i=l-1; i<=r-1; i++){d[i]=c[i-l+1];}for(int i=r; i<n; i++){d[i]=a[i];}/*for(int i=0; i<n; i++){cout<<d[i];}cout<<endl;*/}}}}#endif