E. Money Buys Happiness

Being a physicist, Charlie likes to plan his life in simple and precise terms.

For the next 𝑚 months, starting with no money, Charlie will work hard and earn 𝑥 pounds per month. For the 𝑖-th month (1≤𝑖≤𝑚), there'll be a single opportunity of paying cost 𝑐𝑖 pounds to obtain happiness ℎ𝑖.

Borrowing is not allowed. Money earned in the 𝑖-th month can only be spent in a later 𝑗-th month (𝑗>𝑖).

Since physicists don't code, help Charlie find the maximum obtainable sum of happiness.