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
import sys
n,m=map(int,sys.stdin.readline().split())
M=[m]
A=list(map(int,sys.stdin.readline().split()))
L=[0]*n
inc=False
dec=False
def ALLYes():
    Ans=""
    for i in range(M[0]):
        Ans+="Yes\n"
    sys.stdout.write(Ans)
    return
for i in range(1,n):
    if(A[i]>A[i-1]):
        L[i]=1
        inc=True
    elif(A[i]==A[i-1]):
        L[i]=0
    else:
        L[i]=-1
        dec=True
if(inc==False or dec==False):
    ALLYes()
else:
    neg=L.index(-1)
    pos=L.index(1)
    First=[-1]*n
    for i in range(2,n):
        if(L[i]==0):
            x=max(neg,pos)
            if(x<=i):
                First[i]=x
            elif(min(neg,pos)<=i):
                First[i]=min(neg,pos)
            else:
                First[i]=-1
        if(L[i]==1):
            if(neg>i):
                First[i]=-1
            else:
                First[i]=neg
            pos=i
        if(L[i]==-1):
            if(pos>i):
                First[i]=-1
            else:
                First[i]=pos
            neg=i
    Ans=""
    for i in range(m):
        l,r=map(int,sys.stdin.readline().split())
        r-=1
        if(r-l<1):
            Ans+="Yes\n"
            continue
        if(L[r]==0):
            r=First[r]
            if(r<1):
                Ans+="Yes\n"
                continue
        if(L[r]==1):
            r=First[r]
            if(r<l):
                Ans+="Yes\n"
                continue
            else:
                Ans+="No\n"
                continue
        elif(L[r]==-1):
            r=First[r]
            if(r<l):
                Ans+="Yes\n"
                continue
            r=First[r]
            if(r<l):
                Ans+="Yes\n"
                continue
            else:
                Ans+="No\n"
                continue
    sys.stdout.write(Ans)
    
    
