#!/usr/bin/python
#invlog by Marion McCoskey
from operator import mod, sub

radlst=[5, 11, 13, 29, 53, 59, 67, \
83, 107, 139, 149, 163, 173, 179, \
227, 269, 293, 317, 347, 373, 389, \
419, 443, 467, 509, 557, 563, 587, \
619, 653, 659, 709, 773, 787, 797, \
853, 907, 1019, 1091, 1109, 1187, 1213, \
1229, 1283, 1307, 1373, 1493, 1499, 1523, \
1571, 1619, 1637, 1733, 1867, 1907, 1949, \
1987, 1997, 2027, 2083, 2099, 2293, 2309, \
2339, 2459, 2467, 2477, 2579, 2659, 2677, \
2683, 2693, 2803, 2819, 2837, 2909, 2957, \
2963, 3019, 3203, 3253, 3347, 3371, 3413, \
3467, 3491, 3533, 3539, 3547, 3581, 3643, \
3677, 3779, 3803, 3947, 3989, 4099, 4133, \
4139, 4157, 4253, 4259, 4283, 4349, 4373, \
4483, 4493, 4507, 4517, 4547, 4723, 4787, \
4813, 5099, 5179, 5189, 5261, 5309, 5387, \
5443, 5483, 5501, 5507, 5557, 5683, 5693, \
5717, 5749, 5813, 5827, 5939, 6011, 6131, \
6173, 6197, 6269, 6277, 6317, 6389, 6547, \
6619, 6653, 6659, 6779, 6827, 6829, 6899, \
6907, 7013, 7027, 7109, 7187, 7331, 7517, \
7523, 7573, 7603, 7643, 7691, 7717, 7883, \
7933, 7949, 8069, 8117, 8147, 8219, 8243, \
8291, 8293, 8387, 8563, 8573, 8627, 8677, \
8699, 8747, 8819, 8923, 8963, 9059, 9173, \
9221, 9227, 9371, 9467, 9533, 9539, 9587]

def eea(a,b):
	v1 = [a,1,0]
	v2 = [b,0,1]
	while v2[0]<>0:
	   p = v1[0]//v2[0]
	   v2, v1 = map(sub,v1,[p*vi for vi in v2]), v2
	return v1

def minv(m,k):
	v = eea(m,k)
	if v[1]>=0:
		return v[1]
	else:
		return k+v[1]
		
def mdiv(dor, dend, rad):
    inv=minv(dend, rad)
    return mod(inv*dor, rad)

def duinvs():
	invs=[]
	lim=len(rads)
	ind=0
	while ind<lim:
		xres=mod(mxms[ind], rads[ind])
		invs.append(minv(xres, rads[ind]))
		ind+=1
	return invs

def dulinvs():
	invs=[]
	lim=len(lrads)
	ind=0
	while ind<lim:
		xres=mod(lcms[ind], lrads[ind])
		invs.append(minv(xres, lrads[ind]))
		ind+=1
	return invs

def euc(ar0, ar1):
    while ar0>0:
        rx=ar1%ar0
        ar1=ar0
        ar0=rx
    return ar1

def ducons():
	mxm=1
	mxms=[]
	lcms=[]
	lcm=1
	logss=[]
	lrads=[]
	linvs=[]
	rads=[]
	for ind in range(lim+1):
		rad=radlst[ind]
		rads.append(rad)
		mxms.append(mxm)
		lcms.append(lcm)
		mxm*=rad
		rad1=rad-1
		com=euc(lcm, rad1)
		lrad=(rad1)/com
		lrads.append(lrad)
		lcm*=lrad
		logs=[0]*rad
		tot=1
		for ind in range(1, rad):
			logs[tot]=ind
			tot<<=1
			if tot>rad:
				tot-=rad
		logss.append(logs)
	return (rads[:lim],  mxms[:lim], lcms[:lim], logss[:lim], lrads[:lim], mxms[-1], lcms[-1])
		
def res2dec(ires):
	lim=len(ires)
	tot=ires[0]
	ind=1
	while ind<lim:
		rad=rads[ind]
		cry=mod(tot, rad)
		dig=mod((ires[ind]-cry)*invs[ind], rad)
		tot+=dig*mxms[ind]
		ind+=1
	return tot
	
def lres2dec(ires):
	lim=len(ires)
	tot=ires[0]
	ind=1
	while ind<lim:
		lrad=lrads[ind]
		cry=mod(tot, lrad)
		dig=mod((ires[ind]-cry)*linvs[ind], lrad)
		tot+=dig*lcms[ind]
		ind+=1
	return tot
	
def dec2res(numd):
	ar=[]
	for rad in rads:
		ar.append(numd%rad)
	return ar
	
def dec2lres(numd):
	ar=[]
	for lrad in lrads:
		ar.append(numd%lrad)
	return ar

def durut(res):
	rut=[]
	for ind in range(len(res)):
		logs=logss[ind]
		rut.append(logs[res[ind]]%lrads[ind])
	return rut
	
def ilgr(pres):
	rut=durut(pres)
	return lres2dec(rut)-1
	
def ilg(val):
	pres=dec2res(val)
	return ilgr(pres)
	
def chk():
	tot=2
	for ind in range(1, xlcm-1):
		print ind, ilg(tot)
		tot<<=1

def shodif(tot):
	prv=0
	while tot<(xlcm<<2):
		log=ilg(tot)
		dif=(log-prv)%xlcm
		print tot, log,dif
		prv=log
		tot<<=1

def dif(tot):
	prv=ilg(tot)
	tot<<=1
	log=ilg(tot)
	return (log-prv)%xlcm

def man():
	for ind in range(xlcm):
		print ind,  ilg(ind)
	
lim=3
dtup=ducons()
rads=dtup[0]
lim=len(rads)
mxms=dtup[1]
lcms=dtup[2]
logss=dtup[3]
lrads=dtup[4]
xmxm=dtup[5]
xlcm=dtup[6]
invs=duinvs()
linvs=dulinvs()
man()