codeforces 651A Joysticks

A. Joysticks

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Friends are going to play console. They have two joysticks and only one charger for them. Initially first joystick is charged at a1 percent and second one is charged at a2 percent. You can connect charger to a joystick only at the beginning of each minute. In one minute joystick either discharges by 2 percent (if not connected to a charger) or charges by 1 percent (if connected to a charger).

Game continues while both joysticks have a positive charge. Hence, if at the beginning of minute some joystick is charged by 1 percent, it has to be connected to a charger, otherwise the game stops. If some joystick completely discharges (its charge turns to 0), the game also stops.

Determine the maximum number of minutes that game can last. It is prohibited to pause the game, i. e. at each moment both joysticks should be enabled. It is allowed for joystick to be charged by more than 100 percent.

Input

The first line of the input contains two positive integers a1 and a2 (1 ≤ a1, a2 ≤ 100), the initial charge level of first and second joystick respectively.

Output

Output the only integer, the maximum number of minutes that the game can last. Game continues until some joystick is discharged.

Examples

input

3 5

output

6

input

4 4

output

5

Note

In the first sample game lasts for 6 minute by using the following algorithm:

• at the beginning of the first minute connect first joystick to the charger, by the end of this minute first joystick is at 4%, second is at 3%;
• continue the game without changing charger, by the end of the second minute the first joystick is at 5%, second is at 1%;
• at the beginning of the third minute connect second joystick to the charger, after this minute the first joystick is at 3%, the second one is at 2%;
• continue the game without changing charger, by the end of the fourth minute first joystick is at 1%, second one is at 3%;
• at the beginning of the fifth minute connect first joystick to the charger, after this minute the first joystick is at 2%, the second one is at 1%;
• at the beginning of the sixth minute connect second joystick to the charger, after this minute the first joystick is at 0%, the second one is at 2%.

After that the first joystick is completely discharged and the game is stopped.

题意是两个手柄吧是，然后只能一个充电，充电效率是1%/min，放电效率是2%/min，然后一分钟开始的的时候决定这一分钟是充电还是放电，充电可以充的超过100%，放电的话到0%就结束，或者在一分钟开始的时候应该放电的那个是1%也结束，因为1 - 2 = -1，只能撑半分钟

每分钟有一次机会可以换充放电的手柄，问两个人最长能坚持多长时间

用循环就可以搞定了，就是注意下0%和1%这两种情况就可以了

注意边界1 1输出0，1 2输出1

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <cstring>
#include <queue>
#include <stack>

using namespace std;

int main()
{
	int a, b;
	scanf("%d%d", &a, &b);
	//保证a < b
	if (a > b) {
		int tem = a;
		a = b;
		b = tem;
	}
	int cou = 0;
	//每次都是电量多的放电到不能再放为止才切换充电器
	//如果较大电量<= 1了，就说明这一分钟完不成了
	while (b > 1) {
		if (b - 2 <= 0) {
			cou++;
			break;
		};
		while (b - 2 > 0) {
			b -= 2;
			a += 1;
			cou++;
		}
		//保证a < b
		if (a > b) {
			int tem = a;
			a = b;
			b = tem;
		}
	}
	printf("%d\n", cou);
	return 0;
}