Xenia is an amateur programmer. Today on the IT lesson she learned about the Hamming distance.

The Hamming distance between two strings s=s₁s₂... s_n and t=t₁t₂... t_n of equal length n is value . Record [s_i≠t_i] is the Iverson notation and represents the following: if s_i≠t_i, it is one, otherwise − zero.

Now Xenia wants to calculate the Hamming distance between two long strings a and b. The first string a is the concatenation of n copies of string x, that is, . The second string b is the concatenation of m copies of string y.

Help Xenia, calculate the required Hamming distance, given n,x,m,y.

The first line contains two integers n and m (1≤n,m≤10¹²). The second line contains a non-empty string x. The third line contains a non-empty string y. Both strings consist of at most 10⁶ lowercase English letters.

It is guaranteed that strings a and b that you obtain from the input have the same length.

Print a single integer − the required Hamming distance.

Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.