Problem:
Score : 300 points

Problem Statement

Snuke loves puzzles.

Today, he is working on a puzzle using S- and c-shaped pieces.
In this puzzle, you can combine two c-shaped pieces into one S-shaped piece, as shown in the figure below:

Snuke decided to create as many Scc groups as possible by putting together one S-shaped piece and two c-shaped pieces.

Find the maximum number of Scc groups that can be created when Snuke has N S-shaped pieces and M c-shaped pieces.

Constraints

1 ≤ N,M ≤ 10^{12}

Input

The input is given from Standard Input in the following format:

N M

Output

Print the answer.

Sample Input 1

1 6

Sample Output 1

2

Two Scc groups can be created as follows:

Combine two c-shaped pieces into one S-shaped piece

Create two Scc groups, each from one S-shaped piece and two c-shaped pieces

Sample Input 2

12345 678901

Sample Output 2

175897

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

# 二分探索で行いたい
N, M = [int(i) for i in input().split()]

low = 0
high =  M // 2

if N * 2 > M / 2:
    output = N
else :
    while abs(low-high) > 1:
        mid = (low+high) // 2
        guess_n = N + mid
        guess_m = M-(2 * mid)
        if guess_n > guess_m // 2 :
            high = mid
        else :
            low = mid

    output = low + N
    
print(output)