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D - Number of Multisets /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

• 多重集合の要素数は N で、要素の総和は K
• 多重集合の要素は全て 1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots 、つまり \frac{1}{2^i} (i = 0,1,\dots) のいずれか。

### 制約

• 1 \leq K \leq N \leq 3000
• 入力される数は全て整数である。

### 入力

N K


### 入力例 1

4 2


### 出力例 1

2


• {1, \frac{1}{2}, \frac{1}{4}, \frac{1}{4}}
• {\frac{1}{2}, \frac{1}{2}, \frac{1}{2}, \frac{1}{2}}

### 入力例 2

2525 425


### 出力例 2

687232272


Score : 600 points

### Problem Statement

You are given two positive integers N and K. How many multisets of rational numbers satisfy all of the following conditions?

• The multiset has exactly N elements and the sum of them is equal to K.
• Each element of the multiset is one of 1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots. In other words, each element can be represented as \frac{1}{2^i}\ (i = 0,1,\dots).

The answer may be large, so print it modulo 998244353.

### Constraints

• 1 \leq K \leq N \leq 3000
• All values in input are integers.

### Input

Input is given from Standard Input in the following format:

N K


### Output

Print the number of multisets of rational numbers that satisfy all of the given conditions modulo 998244353.

### Sample Input 1

4 2


### Sample Output 1

2


The following two multisets satisfy all of the given conditions:

• {1, \frac{1}{2}, \frac{1}{4}, \frac{1}{4}}
• {\frac{1}{2}, \frac{1}{2}, \frac{1}{2}, \frac{1}{2}}

### Sample Input 2

2525 425


### Sample Output 2

687232272