Donation

Bill is a billionaire but very down-to-earth. He finds peace in donating gold coins to charities. He always liked the gold coins he had and used to number them with integers. One day he decided to donate $N$ coins (coins numbered $1$ to $N$) to $C$ charities in the country. But Bill is a very moody person, some day he orders that each charity must receive at least one coin, sometimes he says at le