There are N boys and M girls in a dance school. The teachers are organizing a performance and they need exactly K boy-girl couples for their show. Unfortunately, this is not a straightforward task since some children cannot be paired with each other (due to differences in height, skill, etc.). One of the teachers is a computer science graduate, and has decided to count the number of ways to select K couples.
You are given a String canDance containing exactly N elements, each with exactly M characters. The j-th character of the i-th element of canDance is 'Y' if boy i can be paired with girl j, and 'N' otherwise. Return the number of distinct valid ways to select exactly K boy-girl pairs.