Keith has 10 coins labeled 1 through 10, where the i th coin has weight 2^{i}. The coins are all fair, so the probability of flipping heads on any of the coins is \frac{1}{2}. After flipping all of the coins, Keith takes all of the coins which land heads and measures their total weight, W. If the probability that 137 \leq W \leq 1061 is m / n for coprime positive integers m, n, determine m+n.