Problem Statement

You are given integers R, G, B, and K. How many strings S consisting of R, G, and B satisfy all of the conditions below? Find the count modulo 998244353.

• The number of occurrences of R, G, and B in S are R, G, and B, respectively.
• The number of occurrences of RG as (contiguous) substrings in S is K.

Input

Input is given from Standard Input in the following format:
R G B K

Output

Print the answer.

Constraints

• $1 \leq R,G,B\leq 10^6$
• $0 \leq K \leq \mathrm{min}(R,G)$
• All values in input are integers.

Sample Input 1

2 1 1 1

Sample Output 1

6

The following six strings satisfy the conditions.

• RRGB
• RGRB
• RGBR
• RBRG
• BRRG
• BRGR

Sample Input 2

1000000 1000000 1000000 1000000

Sample Output 2

80957240

Find the count modulo 998244353.

见题面 Input 部分

见题面 Output 部分