#include <bits/stdc++.h>
using namespace std;
using ll = long long;
int main() {
  ll n, m;
  cin >> n >> m;
  vector<ll> a(n);
  for (ll &ai : a) cin >> ai;
  ll cdir = 0;
  ll cst = 0;
  vector<array<ll, 2>> lads;
  int i = 0;
  while (i + 1 < n) {
    ll ndir = a[i] < a[i + 1] ? 0 : a[i] > a[i + 1] ? 1 : cdir;
    if (cdir && !ndir) {
      lads.push_back({cst, i});
      while (a[i - 1] == a[i]) i--;
      cst = i;
    }
    cdir = ndir;
    i++;
  }
  lads.push_back({cst, n - 1});
  while (m--) {
    ll l, r;
    cin >> l >> r;
    --l;
    --r;
    auto it =
        --lower_bound(lads.begin(), lads.end(), (array<ll, 2>){l, (ll)1e9});
    auto lad = *it;
    if (r <= lad[1])
      cout << "Yes" << endl;
    else
      cout << "No" << endl;
  }
}

### Prompt

Your challenge is to write a cpp solution to the following problem:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
int main() {
  ll n, m;
  cin >> n >> m;
  vector<ll> a(n);
  for (ll &ai : a) cin >> ai;
  ll cdir = 0;
  ll cst = 0;
  vector<array<ll, 2>> lads;
  int i = 0;
  while (i + 1 < n) {
    ll ndir = a[i] < a[i + 1] ? 0 : a[i] > a[i + 1] ? 1 : cdir;
    if (cdir && !ndir) {
      lads.push_back({cst, i});
      while (a[i - 1] == a[i]) i--;
      cst = i;
    }
    cdir = ndir;
    i++;
  }
  lads.push_back({cst, n - 1});
  while (m--) {
    ll l, r;
    cin >> l >> r;
    --l;
    --r;
    auto it =
        --lower_bound(lads.begin(), lads.end(), (array<ll, 2>){l, (ll)1e9});
    auto lad = *it;
    if (r <= lad[1])
      cout << "Yes" << endl;
    else
      cout << "No" << endl;
  }
}

```