// Hacker Cup 2017 // Qualification Round // Fighting The Zombie // Wesley May import java.util.*; public class FightingTheZombie { static int H; public static void main(String args[]) { double EPS = 0.000001; Scanner scan = new Scanner(System.in); int T = scan.nextInt(); for(int ca=1;ca <= T;ca++) { H = scan.nextInt(); int S = scan.nextInt(); Spell[] a = new Spell[S]; for(int i=0;i < S;i++) { String str = scan.next(); int X, Y, Z; int didx = str.indexOf("d"); int plusidx = str.indexOf("+"); int minusidx = str.indexOf("-"); X = Integer.parseInt(str.substring(0, didx)); if(plusidx >= 0) { Y = Integer.parseInt(str.substring(didx+1, plusidx)); Z = Integer.parseInt(str.substring(plusidx)); } else if(minusidx >= 0) { Y = Integer.parseInt(str.substring(didx+1,minusidx)); Z = Integer.parseInt(str.substring(minusidx)); } else { Y = Integer.parseInt(str.substring(didx+1)); Z = 0; } a[i] = new Spell(X, Y, Z); } Arrays.sort(a); System.out.printf("Case #%d: %.6f\n", ca, a[0].p); } } static class Spell implements Comparable { int x, y, z; public double p; double[][] dp; public Spell(int ix, int iy, int iz) { x = ix; y = iy; z = iz; int newH = H - z; if(newH <= 0) { p = 1; return; } dp = new double[newH+1][x+1]; for(int i=0;i < dp.length;i++) Arrays.fill(dp[i], -1); p = f(newH, x); } private double f(int h, int d) { if(h <= 0) return 1; if(d == 0) return 0; if(dp[h][d] >= 0) return dp[h][d]; double ans = 0; for(int i=1;i <= y;i++) { ans += (1.0 / y) * f(h-i, d-1); } return dp[h][d] = ans; } public int compareTo(Spell that) { if(this.p > that.p) return -1; if(this.p < that.p) return 1; return 0; } } }