A11311. Anna and the Valentine's Day Gift
编程题
普及/提高-
知识点
题目描述
Sasha gave Anna a list $a$ of $n$ integers for Valentine's Day. Anna doesn't need this list, so she suggests destroying it by playing a game.
Players take turns. Sasha is a gentleman, so he gives Anna the right to make the first move.
- On her turn, Anna must choose an element $a_i$ from the list and reverse the sequence of its digits. For example, if Anna chose the element with a value of $42$ , it would become $24$ ; if Anna chose the element with a value of $1580$ , it would become $851$ . Note that leading zeros are removed. After such a turn, the number of elements in the list does not change.
- On his turn, Sasha must extract two elements $a_i$ and $a_j$ ( $i \ne j$ ) from the list, concatenate them in any order and insert the result back into the list. For example, if Sasha chose the elements equal to $2007$ and $19$ , he would remove these two elements from the list and add the integer $200719$ or $192007$ . After such a turn, the number of elements in the list decreases by $1$ .
Players can't skip turns. The game ends when Sasha can't make a move, i.e. after Anna's move there is exactly one number left in the list. If this integer is not less than $10^m$ (i.e., $\ge 10^m$ ), Sasha wins. Otherwise, Anna wins.
It can be shown that the game will always end. Determine who will win if both players play optimally.
Players take turns. Sasha is a gentleman, so he gives Anna the right to make the first move.
- On her turn, Anna must choose an element $a_i$ from the list and reverse the sequence of its digits. For example, if Anna chose the element with a value of $42$ , it would become $24$ ; if Anna chose the element with a value of $1580$ , it would become $851$ . Note that leading zeros are removed. After such a turn, the number of elements in the list does not change.
- On his turn, Sasha must extract two elements $a_i$ and $a_j$ ( $i \ne j$ ) from the list, concatenate them in any order and insert the result back into the list. For example, if Sasha chose the elements equal to $2007$ and $19$ , he would remove these two elements from the list and add the integer $200719$ or $192007$ . After such a turn, the number of elements in the list decreases by $1$ .
Players can't skip turns. The game ends when Sasha can't make a move, i.e. after Anna's move there is exactly one number left in the list. If this integer is not less than $10^m$ (i.e., $\ge 10^m$ ), Sasha wins. Otherwise, Anna wins.
It can be shown that the game will always end. Determine who will win if both players play optimally.
输入格式
The first line contains an integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases.
Then follows the description of the test cases.
The first line of each test case contains integers $n$ , $m$ ( $1 \le n \le 2 \cdot 10^5$ , $0 \le m \le 2 \cdot 10^6$ ) — the number of integers in the list and the parameter determining when Sasha wins.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le 10^9$ ) — the list that Sasha gave to Anna.
It is guaranteed that the sum of $n$ for all test cases does not exceed $2 \cdot 10^5$ .
Then follows the description of the test cases.
The first line of each test case contains integers $n$ , $m$ ( $1 \le n \le 2 \cdot 10^5$ , $0 \le m \le 2 \cdot 10^6$ ) — the number of integers in the list and the parameter determining when Sasha wins.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le 10^9$ ) — the list that Sasha gave to Anna.
It is guaranteed that the sum of $n$ for all test cases does not exceed $2 \cdot 10^5$ .
输出格式
For each test case, output:
- "Sasha", if Sasha wins with optimal play;
- "Anna", if Anna wins with optimal play.
- "Sasha", if Sasha wins with optimal play;
- "Anna", if Anna wins with optimal play.
输入输出样例
输入 #1
9 2 2 14 2 3 5 9 56 1 4 10 1 2007 800 1580 4 5 5000 123 30 4 10 10 6 4 6 2 3 1 10 9 10 7 1 1 6 1 1 10 8 9 1 2 9 10 10 2 10 2 4 5 10 10 10 10
输出 #1
Sasha Anna Anna Sasha Sasha Anna Anna Anna Sasha
说明/提示
Consider the first test case.
Anna can reverse the integer $2$ , then Sasha can concatenate the integers $2$ and $14$ , obtaining the integer $214$ , which is greater than $10^2 = 100$ . If Anna had reversed the integer $14$ , Sasha would have concatenated the integers $41$ and $2$ , obtaining the integer $412$ , which is greater than $10^2 = 100$ . Anna has no other possible moves, so she loses.
Anna can reverse the integer $2$ , then Sasha can concatenate the integers $2$ and $14$ , obtaining the integer $214$ , which is greater than $10^2 = 100$ . If Anna had reversed the integer $14$ , Sasha would have concatenated the integers $41$ and $2$ , obtaining the integer $412$ , which is greater than $10^2 = 100$ . Anna has no other possible moves, so she loses.