Frog Jumping

题意翻译

yyb大神仙在数轴的$0$位置。yyb大神仙有两个正整数$a,b$，如果当前yyb大神仙在位置$k$，yyb大神仙可以用神仙的力量将自己传送到$k+a$或者$k-b$位置。 但是yyb大神仙感觉这样很无聊所以打算将自己限制在一段区间里。$f(x)$表示yyb大神仙只能在$[0,x]$区间里移动，从$0$开始能到达的整点数量。yyb大神仙想求$\sum_{i=0}^mf(i)$。

题目描述

A frog is initially at position $ 0 $ on the number line. The frog has two positive integers $ a $ and $ b $ . From a position $ k $ , it can either jump to position $ k+a $ or $ k-b $ . Let $ f(x) $ be the number of distinct integers the frog can reach if it never jumps on an integer outside the interval $ [0, x] $ . The frog doesn't need to visit all these integers in one trip, that is, an integer is counted if the frog can somehow reach it if it starts from $ 0 $ . Given an integer $ m $ , find $ \sum_{i=0}^{m} f(i) $ . That is, find the sum of all $ f(i) $ for $ i $ from $ 0 $ to $ m $ .

输入输出格式

输入格式

The first line contains three integers $ m, a, b $ ( $ 1 \leq m \leq 10^9, 1 \leq a,b \leq 10^5 $ ).

输出格式

Print a single integer, the desired sum.

输入输出样例

输入样例 #1

7 5 3

输出样例 #1

19

输入样例 #2

1000000000 1 2019

输出样例 #2

500000001500000001

输入样例 #3

100 100000 1

输出样例 #3

101

输入样例 #4

6 4 5

输出样例 #4

10

说明

In the first example, we must find $ f(0)+f(1)+\ldots+f(7) $ . We have $ f(0) = 1, f(1) = 1, f(2) = 1, f(3) = 1, f(4) = 1, f(5) = 3, f(6) = 3, f(7) = 8 $ . The sum of these values is $ 19 $ . In the second example, we have $ f(i) = i+1 $ , so we want to find $ \sum_{i=0}^{10^9} i+1 $ . In the third example, the frog can't make any jumps in any case.