Consider the following function f(X), which takes a single positive integer as argument, and returns an integer.</p>

function f(X):
    iterations := 0
    while X is not 1:
        if X is even:
            divide X by 2
        else:
            add 1 to X
        add 1 to iterations
    return iterations

It can be shown that for any positive integer X, this function terminates. Given an interval [L, R], compute the sum

S = f(L) + f(L + 1) + · · · + f(R − 1) + f(R).

입력 형식

The first and only line of input contains two integers L and R (1 ≤ L ≤ R ≤ 10¹⁸).

출력 형식

Output the result S modulo the prime 10⁹ + 7.

예제 입력 1

1 127

예제 출력 1

1083

예제 입력 2

74 74

예제 출력 2

11