Introduction

This problem is reposted with permission from a problem on HackerRank. As nobody had solved it there, the whole set of problem statement, editorial, test cases and solution code was provided for this repost.

Problem Statement

Define FizzBuzz16 as follows (* pseudocode)

function FizzBuzz16(i) {
    if ( i % 15 == 0 ) {
        return "FizzBuzz"
    } else if ( i % 3 == 0 ) {
        return "Fizz"
    } else if ( i % 5 == 0 ) {
        return "Buzz"
    } else {
        return i.toString(16).toUpperCase()
    }
}

* i % 15 == 0 is an expression that evaluates to the boolean value true when the remainder of the integer i divided by 15 equals 0

* i.toString(16).toUpperCase() is an operation that converts the integer i into a string in hexadecimal notation (with uppercase letters)

For example, FizzBuzz16(14) is "E", FizzBuzz16(15) is "FizzBuzz", FizzBuzz16(16) is "10", and FizzBuzz16(251) is "FB"

Define FizzBuzzString16 as follows (* pseudocode)

function FizzBuzzString16(n) {
    s = ""
    for ( i = 1 ; i <= n ; i++ ) {
        s += FizzBuzz16(i)
    }
    return s
}

* i++ is an operation that increases the value of the integer i by 1

* s += is an operation that appends the string on the right-hand side to the end of the string s

For example, FizzBuzzString16(4) is "12Fizz4", and FizzBuzzString16(16) is "12Fizz4BuzzFizz78FizzBuzzBFizzDEFizzBuzz10"

You are given integers $X$ and $Y$. Find the total of the number of characters F and the number of characters B between the $X$-th character and the $Y$-th character (* including the $X$-th and $Y$-th characters) of FizzBuzzString16(1000000000000)

For example, when $X=1,Y=5$, the $1$st to $5$th characters of FizzBuzzString16(1000000000000) are "12Fiz", with $1$ character F and $0$ characters B, for a total of $1$

For example, when $X=3,Y=18$, the $3$rd to $18$th characters of FizzBuzzString16(1000000000000) are "Fizz4BuzzFizz78F", with $3$ characters F and $1$ character B, for a total of $4$

* Just in case, code corresponding to the definitions of FizzBuzz16 and FizzBuzzString16 in languages other than pseudocode is provided below (click each button to expand)

#include <sstream>

std::string to_hex_string(int64_t i) {
    std::stringstream s;
    s << std::uppercase << std::hex << i;
    return s.str();
}

std::string FizzBuzz16(int64_t i) {
    if (i % 15 == 0) {
        return "FizzBuzz";
    } else if (i % 3 == 0) {
        return "Fizz";
    } else if (i % 5 == 0) {
        return "Buzz";
    } else {
        return to_hex_string(i);
    }
}

std::string FizzBuzzString16(int64_t n) {
    std::string s = "";
    for (int64_t i = 1; i <= n; i++) {
        s += FizzBuzz16(i);
    }
    return s;
}

def FizzBuzz16(i):
    if i % 15 == 0:
        return "FizzBuzz"
    elif i % 3 == 0:
        return "Fizz"
    elif i % 5 == 0:
        return "Buzz"
    else:
        return "%X" % i

def FizzBuzzString16(n):
    s = ""
    for i in range(1,n+1):
        s += FizzBuzz16(i)
    return s

String FizzBuzz16(long i) {
    if (i % 15L == 0L) {
        return "FizzBuzz";
    } else if (i % 3L == 0L) {
        return "Fizz";
    } else if (i % 5L == 0L) {
        return "Buzz";
    } else {
        return String.format("%X", i);
    }
}
 
String FizzBuzzString16(long n) {
    String s = "";
    for (long i = 1L; i <= n; i++) {
        s += FizzBuzz16(i);
    }
    return s;
}

Input

$X$
$Y$

The integer $X$ is given on the first line

The integer $Y$ is given on the second line

Constraints

$1 \le X \le Y \le 1{,}000{,}000{,}000{,}000=10^{12}$

Output

Output the total of the number of characters F and the number of characters B between the $X$-th character and the $Y$-th character (* including the $X$-th and $Y$-th characters) of FizzBuzzString16(1000000000000)

Sample

1
5

1

3
18

4

33
33

1

769
797

11

128153
128159

0

808
277288

52258

1
1000000000000

157481468199