MatKor Cup Preliminary Seat Assignment

Time limit1sMemory limit1024 MB

Summary

Given N participants and M seats, find the expected number of correct seat predictions as a reduced fraction.

Level: Medium4 of 10
Topics: Math, Probability
Solved: No attempts yet

Problem

This MatKor Cup preliminary check-in had $N$ participants in total, and the venue has $M$ prepared seats. Jongwoo assigned each of the $N$ participants a different seat in advance. Dongwoo asked Jongwoo how the seats were assigned.

Jongwoo would not simply tell him. Instead, he asked Dongwoo to predict the seats of all $N$ participants. Dongwoo chose $N$ different seats out of the $M$ seats and predicted each participant's seat.

Find the expected number of participants whose predicted seat matches the seat Jongwoo assigned.

Jongwoo and Dongwoo assign or predict seats with equal probability over all possible cases.

Input

The first line contains $N$ and $M$ ( $1 \le N \le M \le 10^{18}$ ), separated by a space.

Output

Print the expected value on the first line as a reduced fraction ${p\over q}$ ( $1 \le |p|$ ; $2 \le q$ ; $\gcd(|p|,q)=1$ ), written in the form $p$ / $q$ . If the answer is an integer, treat the denominator as 1.

Under the given constraints, the expected value is guaranteed to be rational.

Examples5

Example 1
Input
```
1 1
```
Expected output
```
1/1
```
Example 2
Input
```
1 2
```
Expected output
```
1/2
```
Example 3
Input
```
2 2
```
Expected output
```
1/1
```
Example 4
Input
```
2 4
```
Expected output
```
1/2
```

Example 5

Input

123456789123456789 987654321987654321

Expected output

13717421/109739369