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Problem E
EvenOdd
Consider the following function $f(X)$, which takes a single positive integer as argument, and returns an integer.
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
\[ S = f(L) + f(L+1) + \cdots + f(R-1) + f(R)\enspace . \]Input
The first and only line of input contains two integers $L$ and $R$ ($1 \leq L \leq R \leq 10^{18}$).
Output
Output the result $S$ modulo the prime $10^9+7$.
| Sample Input 1 | Sample Output 1 |
|---|---|
1 127 |
1083 |
| Sample Input 2 | Sample Output 2 |
|---|---|
74 74 |
11 |
