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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 $d_i \lt 0$, 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: $[\underline{3}, \underline{4}, 3, 4, \underline{5}]$, $[\underline{3}, 4, 3, \underline{4}, \underline{5}]$, $[3, 4, \underline{3}, \underline{4}, \underline{5}]$.

伊戈尔有一个整数序列 $d_1, d_2, \dots, d_n$。当他进入教室时，黑板上已写有一个整数 $x$。

伊戈尔使用如下算法生成序列 $p$：

1. 初始时，$p = [x]$；
2. 对每个 $1 \leq i \leq n$，他执行以下操作 $|d_i|$ 次：
   • 若 $d_i \geq 0$，则查看 $p$ 的最后一个元素（记为 $y$），并将 $y + 1$ 追加到 $p$ 末尾；
   • 若 $d_i \lt 0$，则查看 $p$ 的最后一个元素（记为 $y$），并将 $y - 1$ 追加到 $p$ 末尾。

例如，若 $x = 3$，且 $d = [1, -1, 2]$，则 $p = [3, 4, 3, 4, 5]$。

伊戈尔决定计算 $p$ 的最长递增子序列的长度及其个数。

序列 $a$ 是序列 $b$ 的一个子序列，当且仅当 $a$ 可通过从 $b$ 中删除若干（可能为零个或全部）元素得到。

序列 $a$ 是一个递增序列，当且仅当其每个元素（除第一个外）均严格大于前一个元素。

对于 $p = [3, 4, 3, 4, 5]$，最长递增子序列的长度为 $3$，且共有 $3$ 个：$[\underline{3}, \underline{4}, 3, 4, \underline{5}]$、$[\underline{3}, 4, 3, \underline{4}, \underline{5}]$、$[3, 4, \underline{3}, \underline{4}, \underline{5}]$。

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 $d_1, d_2, \ldots, d_n$ ($-10^9 \leq d_i \leq 10^9$).

第一行包含一个整数 $n$（$1 \leq n \leq 50$）——序列 $d$ 的长度。

第二行包含一个整数 $x$（$-10^9 \leq x \leq 10^9$）——黑板上的整数。

第三行包含 $n$ 个整数 $d_1, d_2, \ldots, d_n$（$-10^9 \leq d_i \leq 10^9$）。

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 $998244353$.

输出两个整数：

• 第一个整数应等于排列 $p$ 的最长递增子序列的长度；
• 第二个整数应等于最长递增子序列的个数对 $998244353$ 取模的结果。

你只需输出第二个数对 $998244353$ 取模的结果。

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 $p = [1, 2, \ldots, 2000000000]$.

第一个测试用例已在题目描述中说明。

第二个测试用例中，$p = [100, 101, 102, 103, 104, 105, 104, 103, 102, 103, 104, 105, 106, 107, 108]$。

第三个测试用例中，$p = [1, 2, \ldots, 2000000000]$。