package main

import (
	"bufio"
	"fmt"
	"os"
)

func main() {
	reader := bufio.NewReader(os.Stdin)
	writer := bufio.NewWriter(os.Stdout)
	defer writer.Flush()

	var t int
	fmt.Fscan(reader, &t)
	for i := 0; i < t; i++ {
		var a, b int
		var s string
		fmt.Fscan(reader, &a, &b, &s)

		ans := 0
		zeros := 0
		hasOne := false

		for j := 0; j < len(s); j++ {
			if s[j] == '1' {
				if !hasOne {
					ans += a
					hasOne = true
				} else if zeros > 0 {
					if zeros*b < a {
						ans += zeros * b
					} else {
						ans += a
					}
				}
				zeros = 0
			} else {
				if hasOne {
					zeros++
				}
			}
		}
		fmt.Fprintln(writer, ans)
	}
}