The Slivians are afraid of factoring; it’s just, well, difficult.</p>

Really, they don’t even care about the factors themselves, just how much they sum to.

We can define F(n) as the sum of all of the factors of n; so F(6) = 12 and F(12) = 28. Your task is, given two integers a and b with a ≤ b, to calculate

[S=\sum_{a \le n \le b}{F(n)}]

입력 형식

The input consists of a single line containing space-separated integers a and b (1 ≤ a ≤ b ≤ 10¹²; b − a ≤ 10⁶).

출력 형식

Print S on a single line.

예제 입력 1

101 101

예제 출력 1

102

예제 입력 2

28 28

예제 출력 2

56

예제 입력 3

1 10

예제 출력 3

87

예제 입력 4

987654456799 987654456799

예제 출력 4

987654456800

예제 입력 5

963761198400 963761198400

예제 출력 5

5531765944320

예제 입력 6

5260013877 5260489265

예제 출력 6

4113430571304040