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)

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import sys
import re
import math
import collections
import itertools
import functools

DEBUG = True
DEBUG = False

def dbg(*args):
    if DEBUG:
        print("DBG: ", file=sys.stderr, end="")
        print(*args, file=sys.stderr)


def possible(N, M, k):
    if N >= k:
        return M >= 2*k
    else:
        M -= 2*(k-N)
        return M >= 2*k

def main():
    N, M = map(int, input().split())

    # cc -> S はできるが S -> cc はできない

    # [lo, hi)
    # lo では必ず可能、hiでは必ず不可能
    hi = M // 2
    lo = M // 4 + 1
    while hi - lo > 1:
        mid = (hi + lo) // 2
        if possible(N, M, mid):
            lo = mid
        else:
            hi = mid

    print(lo)

if __name__ == "__main__": main()