Little Susie loves strings. Today she calculates distances between them. As Susie is a small girl after all, her strings contain only digits zero and one. She uses the definition of Hamming distance:

We will define the distance between two strings s and t of the same length consisting of digits zero and one as the number of positions i, such that s_{i} isn't equal to t_{i}. 

As besides everything else Susie loves symmetry, she wants to find for two strings s and t of length n such string p of length n, that the distance from p to s was equal to the distance from p to t.

It's time for Susie to go to bed, help her find such string p or state that it is impossible.


-----Input-----

The first line contains string s of length n. 

The second line contains string t of length n.

The length of string n is within range from 1 to 10^5. It is guaranteed that both strings contain only digits zero and one.


-----Output-----

Print a string of length n, consisting of digits zero and one, that meets the problem statement. If no such string exist, print on a single line "impossible" (without the quotes).

If there are multiple possible answers, print any of them.


-----Examples-----
Input
0001
1011

Output
0011

Input
000
111

Output
impossible



-----Note-----

In the first sample different answers are possible, namely — 0010, 0011, 0110, 0111, 1000, 1001, 1100, 1101.

Difficulty: interview

Starter code:

Solutions:
s = input()
t = input()
sa = s.count('0')
sb = s.count('1')
ta = t.count('0')
tb = t.count('1')
n = len(s)
L = abs(sa - ta) + abs(sb - tb)
L /= 2
if L % 2 == 1:
    print("impossible")
else:
    ans = ''
    c = 0
    for i in range(n):
        if s[i] == t[i]:
            ans += s[i]
        else:
            if c == 0:
                ans += s[i]
                c = 1
            else:
                ans += t[i]
                c = 0
    print(ans)


s1 = input()
s2 = input()
cnt = 0
s = ''
for i in range(len(s1)):
    if s1[i] != s2[i]:
        if cnt % 2 == 0:
            s += s1[i]
        else:
            s += s2[i]
        cnt += 1
    else:
        s += s1[i]
if cnt % 2 == 0:
    print(s)
else:
    print('impossible')


rdl1 = input()
rdl2 = input()

ans = ""
index1 = 0
index2 = 0
for i in range(len(rdl1)):
    if rdl1[i] == rdl2[i]:
        ans += rdl1[i]
    else:
        if index1 > index2:
            ans += rdl2[i]
            index2 += 1
        else:
            ans += rdl1[i]
            index1 += 1
if index1 == index2:
    print(ans)
else:
    print("impossible")


s = input()
t = input()
l = len(s)
p = ''

c = 0
for i in range(l):
    if s[i] != t[i]:
        if c % 2 == 0:
            p += s[i]
        else:
            p += t[i]
        c += 1
    else:
        p += s[i]
        
if c % 2 == 1:
    print('impossible')
else:
    print(p)

a= input()
b= input()

diff= 0
for i in range(len(a)):
    if a[i]!= b[i]:
        diff+= 1
        
if diff%2!= 0:
    print("impossible")
else:
    start= 0
    ans= ""
    for i in range(len(a)):
        if a[i]!= b[i]:
            if start%2== 0:
                ans+= a[i]
            elif start%2== 1:
                ans+= b[i]
            start+= 1
        else:
            ans+= a[i]
    print(ans)

s = input()
t = input()
diffcnt = 0
for i, j in zip(s, t):
    if i != j: diffcnt += 1
if diffcnt % 2 == 1:
    print('impossible')
    return
cnt = 0
ans = []
for i, j in zip(s, t):
    if i == j:
        ans.append(i)
    else:
        ans.append(i if cnt % 2 == 0 else j)
        cnt += 1
print(''.join(ans))
    


S=input()
T=input()
P=''
c=0
A=[0]*len(S)
for i in range(len(S)):
    if S[i]!=T[i]:
        c=c+1
        A[i]=1
if c%2==0:
    for i in range(len(S)):
        if A[i]==1:
            c=c-1
            if c%2==0:
                P=P+T[i]
            else:
                P=P+S[i]
        else:
            P=P+S[i]
    print(P)
else:
    print('impossible')

s = input()
t = input()
if s == t:
    print(s)
    return
p = []
dif = 0
for i in range(len(s)):
    if s[i] != t[i]:
        dif += 1

if dif % 2 == 1:
    print("impossible")
    return
prev = True
for i in range(len(s)):
    if s[i] == t[i]:
        p.append(s[i])
    else:
        if dif:
            p.append(s[i] if prev else t[i])
            prev = False if prev else True
print("".join(p))


s = input()
t = input()

n = len(s)
dist = 0

for i in range(n):
    if (s[i] !=t[i]):
        dist += 1

if dist%2==1:
    print("impossible")
else:
    p = ""
    flag = 0
    for i in range(n):
        if (s[i] != t[i] and flag == 0):
            p += s[i]
            flag = flag^1
        elif (s[i] != t[i] and flag == 1):
            p += t[i]
            flag = flag^1
        elif (s[i] == t[i]):
            p += s[i]
    print(p)