You are given an array a_0, a_1, ..., a_{N-1} of length N. Process Q queries of the following types.

• 0 l r b c: For each $i = l, l+1, \dots, {r - 1}, set a_i \gets b \times a_i + c$.
• 1 l r: Print $\sum_{i = l}^{r - 1} a_i \bmod 998244353$.

Constraints

• $1 \leq N, Q \leq 500000$
• $0 \leq a_i, c < 998244353$
• $1 \leq b < 998244353$
• $0 \leq l < r \leq N$
• All values in Input are integer.

Input

Input is given from Standard Input in the following format:

N Q
a_0 a_1 ... a_{N - 1}
$\textrm{Query}_0$
$\textrm{Query}_1$
:
$\textrm{Query}_{Q - 1}$

Output

For each query of the latter type, print the answer.

Example

Input

5 7
1 2 3 4 5
1 0 5
0 2 4 100 101
1 0 3
0 1 3 102 103
1 2 5
0 2 5 104 105
1 0 5

Output

15
404
41511
4317767

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