import numpy as np

class EllysTwoRatings:
    def getChance(self, N, A, B):
        dist = np.zeros((1001, 1001), dtype=np.float)
        dist[A][B] = 1.0

        mn = np.maximum(1, np.arange(1001) - 100)
        mx = np.minimum(1000, np.arange(1001) + 100)
        denoms = mx - mn + 1

        ans = 0.0
        for n in range(N):
            for i in range(2):
                cumDist = np.cumsum(dist.T / denoms, axis=1)
                for a in range(1, 1000 + 1):
                    dist[a] = cumDist[a][mx] - cumDist[a][mn - 1]
                    ans += dist[a][a]
                    dist[a][a] = 0.0
        return ans