Yuno is taking a walk by her farm when she suddenly notices that a row of corn in the field is not very aesthetically pleasing.

There are $N$ stalks of corn in this row, and their heights are uneven.

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

The problem is as follows:

You are given a sequence $a$ of length $n$ and $m$ operations. Each operation asks whether it is possible to choose two numbers from a given range such that their difference is $x$, their sum is $x$, their product is $x$, or their quotient is $x$ (with no remainder). These four operations are denoted as $1, 2, 3, 4$ respectively.

The two chosen numbers can be from the same position.

Input

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

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

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

$opt$ represents the type of operation, $l$ and $r$ represent the range of the operation, and $x$ represents the value $x$ for this operation.

Output

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

Examples

Input 1

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

Output 1

yuno
yumi
yuno
yuno
yumi

Subtasks

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

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