Description:
Igor had a sequence $$$d_1, d_2, \dots, d_n$$$ of integers. When Igor entered the classroom there was an integer $$$x$$$ written on the blackboard.
Igor generated sequence $$$p$$$ using the following algorithm:
1. initially, $$$p = [x]$$$;
2. for each $$$1 \leq i \leq n$$$ he did the following operation $$$|d_i|$$$ times: if $$$d_i \geq 0$$$, then he looked at the last element of $$$p$$$ (let it be $$$y$$$) and appended $$$y + 1$$$ to the end of $$$p$$$; if $$$d_i < 0$$$, then he looked at the last element of $$$p$$$ (let it be $$$y$$$) and appended $$$y - 1$$$ to the end of $$$p$$$.
For example, if $$$x = 3$$$, and $$$d = [1, -1, 2]$$$, $$$p$$$ will be equal $$$[3, 4, 3, 4, 5]$$$.
Igor decided to calculate the length of the longest increasing subsequence of $$$p$$$ and the number of them.
A sequence $$$a$$$ is a subsequence of a sequence $$$b$$$ if $$$a$$$ can be obtained from $$$b$$$ by deletion of several (possibly, zero or all) elements.
A sequence $$$a$$$ is an increasing sequence if each element of $$$a$$$ (except the first one) is strictly greater than the previous element.
For $$$p = [3, 4, 3, 4, 5]$$$, the length of longest increasing subsequence is $$$3$$$ and there are $$$3$$$ of them: $$$[\underline{3}, \underline{4}, 3, 4, \underline{5}]$$$, $$$[\underline{3}, 4, 3, \underline{4}, \underline{5}]$$$, $$$[3, 4, \underline{3}, \underline{4}, \underline{5}]$$$.
Input Format:
The first line contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the length of the sequence $$$d$$$.
The second line contains a single integer $$$x$$$ ($$$-10^9 \leq x \leq 10^9$$$) — the integer on the blackboard.
The third line contains $$$n$$$ integers $$$d_1, d_2, \ldots, d_n$$$ ($$$-10^9 \leq d_i \leq 10^9$$$).
Output Format:
Print two integers:
- the first integer should be equal to the length of the longest increasing subsequence of $$$p$$$;
- the second should be equal to the number of them modulo $$$998244353$$$.
You should print only the second number modulo $$$998244353$$$.
Note:
The first test case was explained in the statement.
In the second test case $$$p = [100, 101, 102, 103, 104, 105, 104, 103, 102, 103, 104, 105, 106, 107, 108]$$$.
In the third test case $$$p = [1, 2, \ldots, 2000000000]$$$.