The Main Martian Tree grows on Mars. It is a binary tree (a rooted tree, with no more than two sons at each vertex) with $n$ vertices, where the root vertex has the number $1$. Its fruits are the Main Martian Fruits. It's summer now, so this tree does not have any fruit yet.
Autumn is coming soon, and leaves and branches will begin to fall off the tree. It is clear, that if a vertex falls off the tree, then its entire subtree will fall off too. In addition, the root will remain on the tree. Formally: the tree will have some connected subset of vertices containing the root.
After that, the fruits will grow on the tree (only at those vertices which remain). Exactly $x$ fruits will grow in the root. The number of fruits in each remaining vertex will be not less than the sum of the numbers of fruits in the remaining sons of this vertex. It is allowed, that some vertices will not have any fruits.
Natasha wondered how many tree configurations can be after the described changes. Since this number can be very large, output it modulo $998244353$.
Two configurations of the resulting tree are considered different if one of these two conditions is true:
* they have different subsets of remaining vertices;
* they have the same subset of remaining vertices, but there is a vertex in this subset where they have a different amount of fruits.
## Input
The first line contains two integers: $n$ and $x$ ($1 \le n \le 10^5$, $0 \le x \le 10^{18}$) — the size of the tree and the number of fruits in the root.
The $i$\-th of the following $(n-1)$ lines contains two integers $a_i$ and $b_i$ ($1 \le a_i, b_i \le n$) — vertices connected by the $i$\-th edge of the tree.
It is guaranteed that the input data describes a correct binary tree with the root at the vertex $1$.
## Output
Print one number — the number of configurations of the resulting tree modulo $998244353$.
[samples]
## Note
Consider the first example. 
There are $2$ fruits at the vertex $1$. The following $13$ options are possible:
* there is no vertex $2$, there is no vertex $3$; 
* there is no vertex $2$, there are no fruits at the vertex $3$; 
* there is no vertex $2$, there is $1$ fruit at the vertex $3$; 
* there is no vertex $2$, there are $2$ fruits at the vertex $3$; 
* there are no fruits at the vertex $2$, there is no vertex $3$; 
* there are no fruits at the vertex $2$, there are no fruits at the vertex $3$; 
* there are no fruits at the vertex $2$, there is $1$ fruit at the vertex $3$; 
* there are no fruits at the vertex $2$, there are $2$ fruits at the vertex $3$; 
* there is $1$ fruit at the vertex $2$, there is no vertex $3$; 
* there is $1$ fruit at the vertex $2$, there are no fruits at the vertex $3$; 
* there is $1$ fruit at the vertex $2$, there is $1$ fruit at the vertex $3$; 
* there are $2$ fruits at the vertex $2$, there is no vertex $3$; 
* there are $2$ fruits at the vertex $2$, there are no fruits at the vertex $3$. 
Consider the second example. There are $5$ fruits at the vertex $1$. The following $7$ options are possible:
* there is no vertex $2$;
* there are no fruits at the vertex $2$;
* there is $1$ fruit at the vertex $2$;
* there are $2$ fruits at the vertex $2$;
* there are $3$ fruits at the vertex $2$;
* there are $4$ fruits at the vertex $2$;
* there are $5$ fruits at the vertex $2$.
主火星树生长在火星上。它是一棵二叉树（一棵有根树，每个顶点最多有两个子节点），包含 $n$ 个顶点，其中根顶点编号为 $1$。它的果实是主火星果实。现在是夏季，因此这棵树目前还没有任何果实。
秋天即将来临，树叶和枝条将开始从树上掉落。显然，如果一个顶点掉落，那么它的整个子树都会掉落。此外，根节点将保留在树上。形式化地说：树将保留一个包含根节点的连通子集。
之后，果实将在树上生长（仅在保留的顶点上）。根节点恰好会长出 $x$ 个果实。每个剩余顶点上的果实数量不少于其剩余子节点的果实数量之和。允许某些顶点没有果实。
娜塔莎想知道，在上述变化后，有多少种可能的树配置。由于这个数字可能非常大，请对 $998244353$ 取模输出。
两种结果树的配置被认为是不同的，如果满足以下任一条件：
第一行包含两个整数：$n$ 和 $x$（$1 lt.eq n lt.eq 10^5$，$0 lt.eq x lt.eq 10^(18)$）——树的大小和根节点的果实数量。
接下来的 $(n -1)$ 行中，第 $i$ 行包含两个整数 $a_i$ 和 $b_i$（$1 lt.eq a_i, b_i lt.eq n$）——表示第 $i$ 条边连接的两个顶点。
保证输入数据描述了一棵以顶点 $1$ 为根的正确二叉树。
请输出一个数字——结果树的配置数量对 $998244353$ 取模的结果。
考虑第一个例子。
顶点 $1$ 上有 $2$ 个果实。以下 $13$ 种情况是可能的：
考虑第二个例子。顶点 $1$ 上有 $5$ 个果实。以下 $7$ 种情况是可能的：
## Input
第一行包含两个整数：$n$ 和 $x$（$1 lt.eq n lt.eq 10^5$，$0 lt.eq x lt.eq 10^(18)$）——树的大小和根节点的果实数量。第 $i$ 行包含两个整数 $a_i$ 和 $b_i$（$1 lt.eq a_i, b_i lt.eq n$）——表示第 $i$ 条边连接的两个顶点。保证输入数据描述了一棵以顶点 $1$ 为根的正确二叉树。
## Output
请输出一个数字——结果树的配置数量对 $998244353$ 取模的结果。
[samples]
## Note
考虑第一个例子。顶点 $1$ 上有 $2$ 个果实。以下 $13$ 种情况是可能的：没有顶点 $2$，没有顶点 $3$；没有顶点 $2$，顶点 $3$ 上没有果实；没有顶点 $2$，顶点 $3$ 上有 $1$ 个果实；没有顶点 $2$，顶点 $3$ 上有 $2$ 个果实；顶点 $2$ 上没有果实，没有顶点 $3$；顶点 $2$ 上没有果实，顶点 $3$ 上没有果实；顶点 $2$ 上没有果实，顶点 $3$ 上有 $1$ 个果实；顶点 $2$ 上没有果实，顶点 $3$ 上有 $2$ 个果实；顶点 $2$ 上有 $1$ 个果实，没有顶点 $3$；顶点 $2$ 上有 $1$ 个果实，顶点 $3$ 上没有果实；顶点 $2$ 上有 $1$ 个果实，顶点 $3$ 上有 $1$ 个果实；顶点 $2$ 上有 $2$ 个果实，没有顶点 $3$；顶点 $2$ 上有 $2$ 个果实，顶点 $3$ 上没有果实。考虑第二个例子。顶点 $1$ 上有 $5$ 个果实。以下 $7$ 种情况是可能的：没有顶点 $2$；顶点 $2$ 上没有果实；顶点 $2$ 上有 $1$ 个果实；顶点 $2$ 上有 $2$ 个果实；顶点 $2$ 上有 $3$ 个果实；顶点 $2$ 上有 $4$ 个果实；顶点 $2$ 上有 $5$ 个果实。
**Definitions**
Let $ T = (V, E) $ be a rooted binary tree with $ n $ vertices, where $ V = \{1, 2, \dots, n\} $ and vertex $ 1 $ is the root.
Let $ \mathcal{S} \subseteq V $ be a connected subset of vertices such that $ 1 \in \mathcal{S} $ (i.e., $ \mathcal{S} $ induces a connected subtree containing the root).
Let $ f: \mathcal{S} \to \mathbb{Z}_{\geq 0} $ be a function assigning non-negative integer fruit counts to vertices in $ \mathcal{S} $, satisfying:
- $ f(1) = x $,
- For every $ v \in \mathcal{S} \setminus \{1\} $, if $ c_1, c_2 \in \mathcal{S} $ are the (at most two) children of $ v $, then:
$$
f(v) \geq f(c_1) + f(c_2)
$$
(If a child is not in $ \mathcal{S} $, its fruit count is 0.)
**Constraints**
1. $ 1 \leq n \leq 10^5 $
2. $ 0 \leq x \leq 10^{18} $
3. The input defines a valid binary tree rooted at 1.
**Objective**
Count the number of pairs $ (\mathcal{S}, f) $ satisfying the above conditions, modulo $ 998244353 $.