Saving the City

题意翻译

你有一段$01$串，你可以选择花费$B$的代价将一个$0$变为$1$，也可以花费$A$的代价将一段连续的$1$变为$0$，问你最少需要多少代价，才能把整个串都变为$0$

题目描述

Bertown is a city with $ n $ buildings in a straight line. The city's security service discovered that some buildings were mined. A map was compiled, which is a string of length $ n $ , where the $ i $ -th character is "1" if there is a mine under the building number $ i $ and "0" otherwise. Bertown's best sapper knows how to activate mines so that the buildings above them are not damaged. When a mine under the building numbered $ x $ is activated, it explodes and activates two adjacent mines under the buildings numbered $ x-1 $ and $ x+1 $ (if there were no mines under the building, then nothing happens). Thus, it is enough to activate any one mine on a continuous segment of mines to activate all the mines of this segment. For manual activation of one mine, the sapper takes $ a $ coins. He can repeat this operation as many times as you want. Also, a sapper can place a mine under a building if it wasn't there. For such an operation, he takes $ b $ coins. He can also repeat this operation as many times as you want. The sapper can carry out operations in any order. You want to blow up all the mines in the city to make it safe. Find the minimum number of coins that the sapper will have to pay so that after his actions there are no mines left in the city.

输入输出格式

输入格式

The first line contains one positive integer $ t $ ( $ 1 \le t \le 10^5 $ ) — the number of test cases. Then $ t $ test cases follow. Each test case begins with a line containing two integers $ a $ and $ b $ ( $ 1 \le a, b \le 1000 $ ) — the cost of activating and placing one mine, respectively. The next line contains a map of mines in the city — a string consisting of zeros and ones. The sum of the string lengths for all test cases does not exceed $ 10^5 $ .

输出格式

For each test case, output one integer — the minimum number of coins that the sapper will have to pay.

输入输出样例

输入样例 #1

2
1 1
01000010
5 1
01101110

输出样例 #1

2
6

说明

In the second test case, if we place a mine under the fourth building and then activate it, then all mines on the field are activated. The cost of such operations is six, $ b=1 $ coin for placing a mine and $ a=5 $ coins for activating.

题意翻译

你有一段$01$串，你可以选择花费$B$的代价将一个$0$变为$1$，也可以花费$A$的代价将一段连续的$1$变为$0$，问你最少需要多少代价，才能把整个串都变为$0$