limpid studied stochastic processes during the summer vacation, so S-chan decided to set a problem to test him.
S-chan randomly generates $n$ strings, each of length $m$. Specifically, for the $j$-th character of the $i$-th string, each character from 'a' to 'z' is chosen with equal probability.
S-chan wants to know the maximum possible number of nodes and the expected number of nodes in a trie after inserting these $n$ strings (i.e., for any leaf node in the trie, there exists one of the $n$ strings such that the string represented by that leaf node is equal to it).
Since the answers can be very large, you need to output the results modulo $998\,244\,353$.
Note: For the maximum number of nodes, you are not asked for the maximum value modulo $998\,244\,353$, but rather the result of the maximum value modulo $998\,244\,353$.
The definition of a trie is as follows: A trie of size $n$ is a rooted tree with $n$ nodes and $(n-1)$ edges, where each edge is labeled with a character. Every node in the trie represents a string. Let $s(x)$ denote the string represented by node $x$. The root of the trie represents the empty string. Let $u$ be the parent of node $v$, and let $c$ be the character on the edge between $u$ and $v$. Then $s(v) = s(u) + c$. Here, $+$ denotes string concatenation, not standard addition. The strings represented by all nodes are distinct.
Input
The first line contains two integers $n, m$ ($1 \le n, m \le 10^5$), representing the number of strings and the length of each string, respectively.
Output
Output two integers, representing the maximum possible number of nodes and the expected number of nodes, respectively, modulo $998\,244\,353$. For the expected number of nodes, it is guaranteed that the answer can be expressed in the form $\frac{x}{y}$, where $x, y$ are integers and $y \not\equiv 0 \pmod{998\,244\,353}$. You need to output $x \times y^{-1} \pmod{998\,244\,353}$, where $y^{-1}$ is the modular multiplicative inverse of $y$.
Examples
Input 1
1 3
Output 1
4 4
Input 2
2 2
Output 2
5 624641072