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;
const int mod = 1e9 + 7, maxn = 100005, ln = 18;
inline void S(int& n) {
  n = 0;
  int ch = getchar();
  int sign = 1;
  while (ch < '0' || ch > '9') {
    if (ch == '-') sign = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    n = (n << 3) + (n << 1) + ch - '0', ch = getchar();
  }
  n = n * sign;
}
const int inf = int(1e9), shift = 30, etf = mod - 1;
int n, m;
int a[maxn];
vector<int> v[maxn];
void pre() {
  int cnt = 1, flag = 0;
  v[1].push_back(cnt);
  for (int i = 2; i < n + 1; i++) {
    if (!flag) {
      if (a[i] >= a[i - 1])
        v[i].push_back(cnt);
      else {
        flag = 1;
      }
    }
    if (flag) {
      if (a[i] <= a[i - 1])
        v[i].push_back(cnt);
      else {
        flag = 0;
        cnt++;
        i--;
      }
    }
  }
  flag = 0;
  for (int i = 2; i < n; i++) {
    if (a[i] > a[i - 1]) {
      if (flag) {
        for (int j = flag; j < i; j++) {
          v[j].push_back(v[i][0]);
        }
        flag = 0;
      }
    } else if (a[i] < a[i - 1]) {
      flag = i;
    }
  }
}
int main() {
  cin >> n >> m;
  for (int i = 1; i < n + 1; i++) cin >> a[i];
  pre();
  while (m--) {
    int l, r;
    cin >> l >> r;
    if (l == r) {
      cout << "Yes\n";
      continue;
    }
    if (v[l][v[l].size() - 1] == v[r][0])
      printf("Yes\n");
    else
      printf("No\n");
  }
  return 0;
}
