#   Implementation of this algorithm:
#       https://www.reddit.com/r/mathriddles/comments/2v6eaj/doubling_and_adding_1/coey1j7
#
#   Save the code as filename.py. Then run something like
#       python filename.py 8 1

import sys

def getL(k):
    L=1
    Llist = []

    # We first create a list of L's that satisfy the inequalities
    while 2**L+L-2 <= 3*k:
        L = L+1
        if 2**L + L - 2 > k and 2**L + L - 2 < 3*k:
            Llist = Llist + [[L,abs(2**L+L-2*k-2)]]

    # We could use any L for our purpose but we choose one
    # that gets us as close to our goal as possible, by taking
    # as large steps as possible. Note that there's no reason to
    # believe a priori that this actually provides a more efficient
    # solution but it seems reasonable.

    minL = Llist[0][0]
    minval = Llist[0][1]
    for l in Llist:
        if l[1] < minval:
            minL = l[0]
    return minL

def op1(a,b):
    global operations
    operations = operations + 1
    print 2*a,b+1
    return 2*a,b+1

def op2(a,b):
    global operations
    operations = operations + 1
    print a+1,2*b
    return a+1,2*b

#   When (a,b) = (x,x+1) we will use the operations that always work in this case.
def fixone(x):
    return op2(*op2(*op1(*op2(*op1(*op1(*op1(*op1(*op2(*op2(x,x+1))))))))))

#   Figuring out the minimal number of needed operations is interesting.
#   Here's a plot of how well the algorithm at hand does:
#       https://i.imgur.com/z4CssvV.png

def operationsNeeded(k):
    if k == 0:
        return 0
    if k == 1:
        return 10
    L = getL(k)
    return 2*k+2+operationsNeeded(abs(2*k+2-2**L-L))

def makeOperationsNeededData():
    f = open('data','w')
    for i in range(1000000):
        f.write(str(operationsNeeded(i))+"\n")

def main():
    a = int(sys.argv[1])
    b = int(sys.argv[2])
    print a,b

    global operations
    operations = 0

    while 1:
        if a > b:
            print "Swapped the numbers"
            c = a
            a = b
            b = c
        k = b-a

        if k == 0:
            break
        if k == 1:
            a,b = fixone(a)
            break

        for i in range(k):
            a,b = op2(a,b)
        L = getL(k)
        for i in range(k-L+1):
            a,b = op1(a,b)
        a,b = op2(a,b)
        for i in range(L):
            a,b = op1(a,b)

    print "Number of operations:", operations

if __name__ == '__main__':
    main()