Background

Problem Description

Yuno is taking a walk by her farmland. She suddenly finds that a row of corn in the field looks very ugly.

There are a total of $N$ corn plants in this row, and their heights are uneven.

Yuno thinks the cornfield is not beautiful, so she decides to make a data structure problem.

The problem is as follows:

You are given a sequence $a$ of length $n$, with $m$ operations. Each operation queries whether, in a given interval, you can pick two numbers whose difference is $x$, or queries whether, in a given interval, you can pick two numbers whose sum is $x$, or queries whether, in a given interval, you can pick two numbers whose product is $x$, or queries whether, in a given interval, you can pick two numbers whose quotient is $x$ (with no remainder). These four operations are numbered $1,2,3,4$, respectively.

The two chosen numbers may come from the same position.

Input Format

The first line contains two integers $n,m$.

The next line contains $n$ integers representing $a_i$.

The next $m$ lines each contain four integers $opt,l,r,x$.

$opt$ indicates which type of operation it is, $l,r$ specify the interval of the operation, and $x$ is the value $x$ for this operation.

Output Format

For each query, if it is possible, output yuno; otherwise output yumi.

5 5
1 1 2 3 4
4 1 1 1
1 1 2 2
3 1 1 1
3 5 5 16
1 2 3 4

yuno
yumi
yuno
yuno
yumi

Hint

Idea: nzhtl1477, Solution: nzhtl1477, Code: nzhtl1477, Data: nzhtl1477&mrsrz.

For $100\%$ of the testdata, all input numbers are within $[0,10^5]$, and the elements in the sequence are within $[1,10^5]$.

Translated by ChatGPT 5