Balanced Seesaw Array

Bob likes to play seesaw. He thinks that it would be really funny if the seesaw is in a balanced state. It means that the seesaw is not tilted to the left and right. After playing the seesaw, Bob thinks about a problem related to the balanced seesaw.

Let $A = \[a\_1, a\_2, \dots , a\_m]$ denote an array of length $m$. Bob thinks that $\[a\_1, a\_2, \dots , a\_m]$ is a balanced seesaw array if there exists an integer $k$ between $1$ to $m$ such that $\sum\_{i=1}^{m}{(i-k)a\_i} = 0$.

Bob gets an array $A = \[a\_1, a\_2, \dots , a\_n]$ as his birthday gift, and he is curious about whether some non-empty subarray is a balanced seesaw array. More formally, he is interested in whether $\[a\_ℓ , a\_{ℓ+1}, \dots , a\_r]$ is a balanced seesaw array for some specified pair $(ℓ, r)$ where $1 ≤ ℓ ≤ r ≤ n$. Bob also finds that the elements in its array will change by time, it will have the following two types of changes.

1. $a\_ℓ , a\_{ℓ+1}, \dots , a\_r$ are increased by $x$.
2. $a\_ℓ , a\_{ℓ+1}, \dots , a\_r$ are changed to $x$.

For convenience, Bob will give you the array $A = \[a\_1, a\_2, \dots , a\_n]$ first. Then, there are $q$ operations. Each operation will be one of the following three types.

• $1$ $ℓ$ $r$ $x$: means that $a\_ℓ , a\_{ℓ+1}, \dots , a\_r$ are increased by $x$.
• $2$ $ℓ$ $r$ $x$: means that $a\_ℓ , a\_{ℓ+1}, \dots , a\_r$ are changed to $x$.
• $3$ $ℓ$ $r$: means that Bob is curious about whether the subarray $\[a\_ℓ , a\_{ℓ+1}, \dots , a\_r]$ is a balanced seesaw array. You should output “Yes” or “No” for each operation type 3.

The first line of input contains two integers $n$ and $q$. $n$ is the length of the array, and $q$ is the number of operations. The second line contains $n$ integers $a\_i$ to define the array. Each of the following $q$ lines is an operation described in the problem statement.

Please output “Yes” or “No” to indicate whether $\[a\_ℓ , a\_{ℓ+1}, \dots , a\_r]$ is a balanced seesaw array for each type 3 operation.

• $1 ≤ n ≤ 100000$
• $1 ≤ q ≤ 1200000$
• $-1000 ≤ a\_i ≤ 1000$
• $-10000 ≤ x ≤ 10000$
• For $1 ≤ i ≤ n$, you may assume that $|a\_i | ≤ 1.5 × 10^9$ after any operation.
• $1 ≤ ℓ ≤ r ≤ n$