Generalized Leap Year

Normally, whether year $x$ in the Common Era is a leap year is defined as follows.

1. If $x$ is a multiple of 400, it is a leap year.
2. Otherwise, if $x$ is a multiple of 100, it is not a leap year.
3. Otherwise, if $x$ is a multiple of 4, it is a leap year.
4. Otherwise, it is not a leap year.

This can be generalized as follows. Given a sequence $A_1, \dots, A_n$, whether year $x$ in the Common Era is a "generalized leap year" is defined as follows.

1. For the smallest $i$ ($1 \le i \le n$) such that $x$ is a multiple of $A_i$, if $i$ is odd then it is a generalized leap year, and if $i$ is even then it is not.
2. If no such $i$ exists, then if $n$ is odd it is not a generalized leap year, and if $n$ is even it is a generalized leap year.

For example, when $A = [400, 100, 4]$, the generalized leap years for this $A$ are the same as ordinary leap years.

Given a sequence $A_1, \dots, A_n$ and positive integers $l, r$, find the number of positive integers $x$ with $l \le x \le r$ such that year $x$ in the Common Era is a generalized leap year for $A$.

The input consists of at most 50 data sets. Each data set has the following format.

n l r
A1
A2
...
An

The integer $n$ satisfies $1 \le n \le 50$. The integers $l, r$ satisfy $1 \le l \le r \le 4000$. For each $i$, the integer $A_i$ satisfies $1 \le A_i \le 4000$.

The end of the input is marked by a line of three zeros.

For each data set, print the answer on one line.