3011: Fireworks Show 焰火表演
题目描述
It's Independence Day, and Farmer John has taken the cows to the fireworks show. Bessie wonders how much of the show the cows will be able to see since they might not be able to stay for the entire display. The show features C (1 ≤ C ≤ 100) fireworks cannons conveniently numbered 1..C. Cannon i shoots fireworks every Ti (1 ≤ Ti ≤ N) seconds (all times in this task are integer seconds). In a spectacular opening, all cannons first shoot at time 0. Fireworks are visible only during the second in which they are launched from the cannon. The cows will stay at the show from time 1 through time N (1 ≤ N ≤ 2,000,000). Help Bessie figure out how many different times the cows will be able to see fireworks during the time period that they are at the show.
输入
* Line 1: Two space-separated integers: C and N. * Lines 2..C + 1: Line i+1 contains the single integer Ti.
输出
* Line 1: A single integer that is the number of distinct seconds in the time interval from 1 through N that the cows will be able to see fireworks.
样例输入 复制
2 20
4
6样例输出 复制
7提示
Input Details
The show features 2 cannons: one shooting fireworks every 4 seconds, the other shooting every 6 seconds. The cows will stay at the show from time 1 to time 20. Below is a chart showing the fireworks launches and the time the cows are present.
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 2 2 2 ... 1 1 2 1 1 1 2 1 1 ... +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ ... 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ...
Output Details
There will be fireworks at times 4, 6, 8, 12, 16, 18, and 20, for a total of 7 distinct times. (Note that time 12, where both cannons shoot fireworks simultaneously, is only counted once.) See the graph above.