You've got an array, consisting of n integers a1, a2, ..., an. Also, you've got m queries, the i-th query is described by two integers li, ri. Numbers li, ri define a subsegment of the original array, that is, the sequence of numbers ali, ali + 1, ali + 2, ..., ari. For each query you should check whether the corresponding segment is a ladder. 

A ladder is a sequence of integers b1, b2, ..., bk, such that it first doesn't decrease, then doesn't increase. In other words, there is such integer x (1 ≤ x ≤ k), that the following inequation fulfills: b1 ≤ b2 ≤ ... ≤ bx ≥ bx + 1 ≥ bx + 2... ≥ bk. Note that the non-decreasing and the non-increasing sequences are also considered ladders.

Input

The first line contains two integers n and m (1 ≤ n, m ≤ 105) — the number of array elements and the number of queries. The second line contains the sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 109), where number ai stands for the i-th array element.

The following m lines contain the description of the queries. The i-th line contains the description of the i-th query, consisting of two integers li, ri (1 ≤ li ≤ ri ≤ n) — the boundaries of the subsegment of the initial array.

The numbers in the lines are separated by single spaces.

Output

Print m lines, in the i-th line print word "Yes" (without the quotes), if the subsegment that corresponds to the i-th query is the ladder, or word "No" (without the quotes) otherwise. 

Examples

Input

8 6
1 2 1 3 3 5 2 1
1 3
2 3
2 4
8 8
1 4
5 8


Output

Yes
Yes
No
Yes
No
Yes
#include <bits/stdc++.h>
using namespace std;
long long a[100009];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n, q, x, y, i = 1, l, r;
  cin >> n >> q;
  while (i <= n) cin >> a[i++];
  i = 1;
  set<long long> s, d;
  while (i <= n) {
    if (a[i] > a[i - 1]) {
      while (i <= n && a[i] >= a[i - 1]) i++;
      s.insert(i - 1);
    } else if (a[i] < a[i - 1]) {
      while (i <= n && a[i] <= a[i - 1]) i++;
      d.insert(i - 1);
    } else
      i++;
  }
  s.insert(LLONG_MAX);
  d.insert(LLONG_MAX);
  while (q--) {
    cin >> l >> r;
    if (l == r) {
      cout << "Yes\n";
      continue;
    }
    x = *s.lower_bound(l);
    y = *d.lower_bound(l);
    if (x == l) {
      if (y >= r)
        cout << "Yes\n";
      else
        cout << "No\n";
      continue;
    }
    if (y == l) {
      if (x >= r)
        cout << "Yes\n";
      else {
        auto it = d.lower_bound(l);
        it++;
        y = *it;
        if (y >= r)
          cout << "Yes\n";
        else
          cout << "No\n";
      }
      continue;
    }
    if (x < y) {
      if (y >= r)
        cout << "Yes\n";
      else
        cout << "No\n";
      continue;
    }
    if (y >= r) {
      cout << "Yes\n";
      continue;
    }
    if (a[y] == a[l]) {
      auto it = d.lower_bound(l);
      it++;
      if (*it >= r)
        cout << "Yes\n";
      else
        cout << "No\n";
    } else
      cout << "No\n";
  }
}
