SPOJ in Gyumri

   Mr. A proposes to his son the following problem:

   ”Consider two integers n₁ and n₂ such that 1≤n₁<n₂≤10⁴.  Using  the  function  (where N^* is the set of positive integers) we define the set

   We also define a set of pairs as follows:

   Consider the formula:

where gcd(m₁,m₂) is the greatest common divisor of m₁ and m₂. The problem asks to find the number R(n₁,n₂).”

   Solve the problem proposed by Mr. A.

Input

   The input file consists of a single line having the values for n₁ and n₂, separated by exactly one space.

Output

   For each test, the result will be written to standard output and consists of the value of R(n₁,n₂).

Examples