package main

// add binary
// func minInt(x, y int) int {
// 	if x < y {
// 		return x
// 	}
// 	return y
// }

const one, zero = byte('1'), byte('0')

func add3Bi(x, y, z byte) (sum, remain byte) {
	switch x + y + z - 3*zero {
	case 0:
		return zero, zero
	case 1:
		return one, zero
	case 2:
		return zero, one
	case 3:
		return one, one
	default:
		return
	}
}

func reverseStr(s string) string {
	runes := []rune(s)
	for from, to := 0, len(s)-1; from < to; from, to = from+1, to-1 {
		runes[from], runes[to] = runes[to], runes[from]
	}
	return string(runes)
}

func addBinary(a string, b string) string {
	la, lb := len(a)-1, len(b)-1
	sum, remain := zero, zero
	res := make([]rune, 0)
	for i := 0; i <= minInt(la, lb); i++ {
		sum, remain = add3Bi(a[la-i], b[lb-i], remain)
		res = append(res, rune(sum))
	}
	lc := 0
	var c string
	if la < lb {
		c = b
		lc = lb
	} else {
		c = a
		lc = la
	}
	for i := minInt(la, lb) + 1; i <= lc; i++ {
		sum, remain = add3Bi(zero, c[lc-i], remain)
		res = append(res, rune(sum))
	}
	if remain == one {
		res = append(res, rune(one))
	}
	return reverseStr(string(res))
}