Digit Powers

There are a certain group of numbers, such that if you take the sum of each digit raised to the $k$ th power, where $k$ is the number of digits in the number, you will get the original number. In other words, they are numbers that are equal to the sum of the digits raised to the power of the number of digits. For example, $153 \rightarrow 1^{3} + 5^{3} + 3^{3} = 153$ . All single digit positive integers have this property, but no two digit numbers do. There are only four three digit numbers that work: $153$ , $370$ , $371$ , and $?$ . Find the fourth.