Background

The annual Christmas is approaching. Every year, Little E receives many gifts, and he also gives out many gifts. Different people have different importance in Little E's heart, and those who are more important receive more gifts.

Problem Description

Little E has purchased $n$ gifts from the store, intending to give them to $m$ people, where the number of gifts for the $i$-th person is $w_i$. Please help calculate the number of ways to distribute the gifts (two schemes are considered different if and only if someone receives different gifts in the two schemes). Since the number of schemes may be very large, you only need to output the result modulo $P$.

Input Format

The first line contains an integer $P$, representing the modulus.
The second line contains two integers $n$ and $m$, representing the number of gifts Little E bought and the number of people receiving gifts, respectively.
From the 3rd to the $(m + 2)$-th line, each line contains an integer, where the $(i + 2)$-th line's integer $w_i$ represents the number of gifts for the $i$-th person.

Output Format

If there is no feasible scheme, output Impossible; otherwise, output an integer representing the number of schemes modulo $P$.

Sample Input and Output

Sample Input #1

100
4 2
1
2

Sample Output #1

12

Sample Input #2

100
2 2
1
2

Sample Output #2

Impossible

Notes

Sample 1 Explanation

The gifts for the first and second persons are separated by /. The 12 schemes are detailed as follows:

1/23 1/24 1/34
2/13 2/14 2/34
3/12 3/14 3/24
4/12 4/13 4/23

Data Size and Constraints

Let $P = \prod_{i=1}^t p_i^{c_i}$, where $p_i$ are prime numbers.

For 15% of the data, $n \leq 15$, $m \leq 5$, $p_i^{c_i} \leq 10^5$.

For the remaining 85% of the data, about 60% of the data satisfy $t \leq 2$, $c_i = 1$, $p_i \leq 10^5$, and about 30% of the data satisfy $p_i \leq 200$.

For 100% of the data, $1 \leq n \leq 10^9$, $1 \leq m \leq 5$, $1 \leq p_i^{c_i} \leq 10^5$, $1 \leq w_i \leq P \leq 10^9$.

见题面 Input 部分

见题面 Output 部分