Cornfield Query Challenge

Yuina, while taking a walk by her farm, noticed that one row of her cornfield wasn't very beautiful due to the uneven heights of the $N$ corn stalks. To improve the aesthetics of the cornfield, she devised a data structure problem.

You are given a sequence $a$ of length $n$ and $m$ queries. Each query is one of four types, identified by an operation number:

1. Query type 1: Given an interval $[L, R]$ and an integer $x$, determine if you can choose two (not necessarily distinct) numbers from the interval such that their difference is (x) (i.e. if there exists $a$ and $b$ in the interval with (b - a = x)).

2. Query type 2: Given an interval $[L, R]$ and an integer $x$, determine if you can choose two numbers such that their sum is (x) (i.e. $a + b = x$). Note that if (x) is even, selecting the same element twice is allowed if (2a = x).

3. Query type 3: Given an interval $[L, R]$ and an integer $x$, determine if you can choose two numbers whose product is (x) (i.e. $a\times b = x$). Again, the same element may be chosen twice.

4. Query type 4: Given an interval $[L, R]$ and an integer $x$, determine if you can choose two numbers (with the divisor non-zero) such that the quotient is (x) (i.e. $a/b = x$, where the division has no remainder). Note that if (x=1) then any nonzero element chosen twice satisfies the condition; also, for (x=0), you must have $a=0$ and $b\neq0$.

For each query, print YES if such a pair exists, otherwise print NO.

inputFormat

The first line contains two integers $n$ and $m$, denoting the length of the sequence and the number of queries, respectively.

The second line contains $n$ integers representing the sequence $a$.

Each of the next $m$ lines contains four integers: $op$, $L$, $R$, and $x$, representing the query type and its parameters.

outputFormat

For each query, print a single line containing YES if there exists a pair of numbers in the specified interval satisfying the condition for that query, otherwise print NO.

sample

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

YES
YES
YES
YES
YES