XOR of Binomial Sum

Given two integers n and m (with m ≤ n), define

\[ F(a,b)=\sum_{i=0}^{b}\binom{b}{i}\binom{n-i}{a} \]

for integers 1 ≤ a, b ≤ m. Compute

\[ X=\bigoplus_{a=1}^{m}\bigoplus_{b=1}^{m}\Bigl(F(a,b)\bmod 998244353\Bigr), \]

where \(\oplus\) denotes the bitwise XOR operation. Output X.

inputFormat

The first line contains two integers n and m where 1 ≤ m ≤ n.

outputFormat

Output a single integer, the value of X computed as described above.

sample

5 1

9

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