# Alternating List Solved

The objective of this problem is to test the students’ understanding on Singly Linked List.

Problem Description

A list is alternating if its elements alternate between positive and negative. For example:

You are given a linked list (original) and Q updates. For each update, check if the updated linked list is alternating. It is guaranteed that the elements in the linked list before and after update will not be 0.

There are 3 valid update operations, as explained below. Note that the indices of a list begin with one, not zero.

1. M <index <size: Move a block of elements of length <size starting at index <index to the back of the list. For example, let the current linked list be [1, 3, 5, 4, 2, 6]. The operation “M 2 3” moves [3, 5, 4] to the end of the linked list. The updated linked list is [1, 2, 6, 3, 5, 4].

2. R <index <size: Remove a block of elements of length <size starting at index <index from the linked list. For example, let the current linked list be [1, 3, 5, 4, 6, 7]. The operation “R 2 4” removes [3, 5, 4, 6] from the list. After performing the operation, we will have [1, 7].

3. A <index <size <value: Add the elements between index <index and <index + size – 1 (inclusive) with <value. For example, let the current linked list be [1, -3, -5, 6, 10]. The operation “A 1 3 4” adds [-3, -5, 6] with value 4. The updated linked list is [1, 1, -1, 10, 10].

* It is guaranteed that <size will not cause the index to go beyond the size of the Linked List (i.e. size + index – 1 LinkedList.size). For every operation, <size is positive.

Input

The first line of the input contains 2 integers N (1 <= N <= 100) and Q (1 <= Q <= 100), where N is the size of the original linked list and Q the number of updates. The next line contains N integers, denoting the elements in the original linked list. The next Q lines are the update operations.

Output

Print “YES” if the updated linked list is alternating, otherwise print “NO”.

Alternating lists

Non-alternating lists

[ -1, 10, -2, 3, -5 ]

[ -4, 2, -3, -7, 6 ]

[ 1, -2, 3, -4 ]

[ 4, 3 ]

[ 3 ]

[ 8, -8, 3, 4, -1 ]

[ ] (empty list)

[ -2, -4, -6 ]

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Sample Input

4 4

1 -2 3 -4

M 1 3

A 1 1 14

R 2 2

A 2 1 -11

Sample Output

YES

NO NO YES

Explanation

N = 4 and Q = 4.

Update 1: [1, -2, 3, -4] [-4, 1, -2, 3] and [-4, 1, -2, 3] is alternating.

Update 2: [-4, 1, -2, 3] [10, 1, -2, 3] and [10, 1, -2, 3] is NOT alternating.

Update 3: [10, 1, -2, 3] [10, 3] and [10, 3] is NOT alternating.

Update 4: [10, 3] [10, -8] is alternating.

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Problem Description

A list is alternating if its elements alternate between positive and negative. For example:

You are given a linked list (original) and Q updates. For each update, check if the updated linked list is alternating. It is guaranteed that the elements in the linked list before and after update will not be 0.

There are 3 valid update operations, as explained below. Note that the indices of a list begin with one, not zero.

1. M <index <size: Move a block of elements of length <size starting at index <index to the back of the list. For example, let the current linked list be [1, 3, 5, 4, 2, 6]. The operation “M 2 3” moves [3, 5, 4] to the end of the linked list. The updated linked list is [1, 2, 6, 3, 5, 4].

2. R <index <size: Remove a block of elements of length <size starting at index <index from the linked list. For example, let the current linked list be [1, 3, 5, 4, 6, 7]. The operation “R 2 4” removes [3, 5, 4, 6] from the list. After performing the operation, we will have [1, 7].

3. A <index <size <value: Add the elements between index <index and <index + size – 1 (inclusive) with <value. For example, let the current linked list be [1, -3, -5, 6, 10]. The operation “A 1 3 4” adds [-3, -5, 6] with value 4. The updated linked list is [1, 1, -1, 10, 10].

* It is guaranteed that <size will not cause the index to go beyond the size of the Linked List (i.e. size + index – 1 LinkedList.size). For every operation, <size is positive.

Input

The first line of the input contains 2 integers N (1 <= N <= 100) and Q (1 <= Q <= 100), where N is the size of the original linked list and Q the number of updates. The next line contains N integers, denoting the elements in the original linked list. The next Q lines are the update operations.

Output

Print “YES” if the updated linked list is alternating, otherwise print “NO”.

Alternating lists

Non-alternating lists

[ -1, 10, -2, 3, -5 ]

[ -4, 2, -3, -7, 6 ]

[ 1, -2, 3, -4 ]

[ 4, 3 ]

[ 3 ]

[ 8, -8, 3, 4, -1 ]

[ ] (empty list)

[ -2, -4, -6 ]

Page 2 of 2

Sample Input

4 4

1 -2 3 -4

M 1 3

A 1 1 14

R 2 2

A 2 1 -11

Sample Output

YES

NO NO YES

Explanation

N = 4 and Q = 4.

Update 1: [1, -2, 3, -4] [-4, 1, -2, 3] and [-4, 1, -2, 3] is alternating.

Update 2: [-4, 1, -2, 3] [10, 1, -2, 3] and [10, 1, -2, 3] is NOT alternating.

Update 3: [10, 1, -2, 3] [10, 3] and [10, 3] is NOT alternating.

Update 4: [10, 3] [10, -8] is alternating.

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