CF926F Mobile Communications

A sum of $ p $ rubles is charged from Arkady's mobile phone account every day in the morning. Among the following $ m $ days, there are $ n $ days when Arkady will top up the account: in the day $ d_{i} $ he will deposit $ t_{i} $ rubles on his mobile phone account. Arkady will always top up the account before the daily payment will be done. There will be no other payments nor tops up in the following $ m $ days. Determine the number of days starting from the $ 1 $ -st to the $ m $ -th such that the account will have a negative amount on it after the daily payment (i. e. in evening). Initially the account's balance is zero rubles.

The first line contains three integers $ n $ , $ p $ and $ m $ ( $ 1

Print the number of days from the $ 1 $ -st to the $ m $ -th such that the account will have a negative amount on it after the daily payment.

In the first example the balance will change as following (remember, initially the balance is zero): 1. in the first day $ 6 $ rubles will be charged, the balance in the evening will be equal to $ -6 $ ; 2. in the second day Arkady will deposit $ 13 $ rubles, then $ 6 $ rubles will be charged, the balance in the evening will be equal to $ 1 $ ; 3. in the third day $ 6 $ rubles will be charged, the balance in the evening will be equal to $ -5 $ ; 4. in the fourth day Arkady will deposit $ 20 $ rubles, then $ 6 $ rubles will be charged, the balance in the evening will be equal to $ 9 $ ; 5. in the fifth day $ 6 $ rubles will be charged, the balance in the evening will be equal to $ 3 $ ; 6. in the sixth day $ 6 $ rubles will be charged, the balance in the evening will be equal to $ -3 $ ; 7. in the seventh day Arkady will deposit $ 9 $ rubles, then $ 6 $ rubles will be charged, the balance in the evening will be equal to $ 0 $ . Thus, in the end of the first, third and sixth days the balance will be negative in the end of the day.