P10707 Eternity (Eternity)

>$$Walking among the world,$$ > >$$may not be angels.$$ > >$$Those who bring disaster,$$ > >$$may not be demons.$$ > >$$A demon's tears are treasured by angels,$$ > >$$and an angel's purity is guarded by demons.$$ > >$$Perhaps,$$ > >$$this is the best ending.$$

Some preliminary definitions: - Elements in a multiset must be non-negative integers. - The size of a multiset is the number of elements in the multiset. - For a multiset of size $x$, let its elements be $a_1,a_2\dots a_x$. Then the **value** of this multiset is $a_1\oplus a_2\oplus \dots \oplus a_x$, that is, the **xor sum** of all elements in the multiset. Now given $n,m$. How many different multisets $S$ of size $n$ satisfy: $$\max\limits_{T \subseteq S,T\ne \emptyset}{Q_T}=m$$ where $Q_T$ is the **value** of multiset $T$. **Note: Due to the nature of multisets, multisets with the same numbers but different orders are considered the same multiset. For example, $\left \{ 1,2,3 \right \} $ and $\left \{ 3,2,1 \right \} $ are the same multiset.** Output the number of different multisets modulo $998244353$. It can be proven that the number of such multisets is finite.

The first line contains two integers, representing $n$ and $m$.

One line with one integer, the answer modulo $998244353$.

#### Sample Explanation In sample 1, the $13$ valid multisets are: $$(0,0,5)$$, $$(0,1,4)$$, $$(0,1,5)$$, $$(0,4,5)$$, $$(0,5,5)$$, $$(1,1,4)$$, $$(1,1,5)$$, $$(1,4,4)$$, $$(1,4,5)$$, $$(1,5,5)$$, $$(4,4,5)$$, $$(4,5,5)$$, $$(5,5,5)$$. #### Constraints | subtask ID | $n$ | $m$ | Special Property | Score | | :----------: | :----------: | :----------: | :----------: | :-----: | | $0$ | $\le 10$ | $\le 10$ | $-$ | $10$ | | $1$ | $\le 10^5$ | $