Kutus loves even number. Girl friend of Kutus, name Putus makes an interesting problem for Kutus to testing his even number knowledge. Putus gives an integer array A, consisting of N number.

Putus asked Kutus to process the following three types of queries on this array accurately and efficiently.

• 0 X V: add V to the Xth element of array. i.e. AX = AX + V.
• 1 L R V: replace all the element in range L to R with V.
• 2 L R: Find out whether all elements frequency in the range L to R is/are even or not

Input

Input start with an integer T, which denotes the number of test case. Each case contains 2 space separated integer N and Q denoting the size of array A and the number of queries to be performed.

Next line contains N space separated integers denoting the elements of array A. Each of the next Q lines of input contains a query having one of the mentioned three types. There will be no more than fifty update operation (type 0 and type 1).

Output

For each case print the case number and print the answer. If all elements frequency in the range L to R is/are even, then answer will be ‘Yes’ otherwise answer will be ‘No’.

Constraints

T <= 10

1 <= N <= 100000

1 <= Q <= 100000

0 <= Ai , V <= 100000

1 <= L <= R <= N

Example

Input:
1
5 6
1 2 2 3 2
2 2 3
0 5 1
2 2 5
2 1 5
1 1 3 2
2 1 5

Output:
Case 1:
Yes
Yes
No
No