package adv2017; import java.awt.geom.Point2D; import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.InputMismatchException; // formatしないやつ public class N620_4 { InputStream is; PrintWriter out; String INPUT = ""; void solve() { int U = ni(); if(!(1 <= U && U <= 1000))throw new AssertionError("U"); for(;U > 0;U--){ int T = ni(); double P = nd(); double omega = nd(); double v = nd(); double gx = nd(); double gy = nd(); if(!(1 <= T && T <= 15))throw new AssertionError("T"); if(!(0 <= P && P <= 1e9))throw new AssertionError("P"); if(!(-10 <= omega && omega <= 10))throw new AssertionError("omega"); if(!(-10 <= v && v <= 10))throw new AssertionError("v"); if(!(-100 <= gx && gx <= 100))throw new AssertionError("gx"); if(!(-100 <= gy && gy <= 100))throw new AssertionError("gy"); /* (1+v -ω ux) (ω 1+v uy) (0 0 1) * */ double[][] M = { {1+v, -omega}, {omega, 1+v} }; double[][] E = { {1, 0}, {0, 1} }; double[][][] MS = new double[T+1][][]; MS[0] = E; for(int i = 1;i <= T;i++){ MS[i] = mul(MS[i-1], M); } double[][] Q = new double[2*T+2][2*T+2]; for(int i = 0;i < 2*T;i++){ Q[i][i] = 1; } // Q = I // c = 0 // E = MS[T-1] MS[T-2] MS[T-3] ... for(int i = 0;i < T;i++){ for(int j = 0;j < 2;j++){ for(int k = 0;k < 2;k++){ Q[2*i+k][2*T+j] = Q[2*T+j][2*i+k] = MS[T-1-i][j][k]; } } } double[] d = new double[2*T+2]; d[2*T] = gx - MS[T][0][0]; d[2*T+1] = gy - MS[T][1][0]; double[] x = solve(Q, d); // check(omega, v, x, T, gx, gy, P); for(int i = 0;i < 2*T;i+=2){ out.print(dtos(x[i], 14)); out.print(" "); out.println(dtos(x[i+1], 14)); // out.printf("%.14f %.14f\n", x[i], x[i+1]); } } } public static String dtos(double x, int n) { StringBuilder sb = new StringBuilder(); if(x < 0){ sb.append('-'); x = -x; } x += Math.pow(10, -n)/2; // if(x < 0){ x = 0; } sb.append((long)x); sb.append("."); x -= (long)x; for(int i = 0;i < n;i++){ x *= 10; sb.append((int)x); x -= (int)x; } return sb.toString(); } static void check(double omega, double V, double[] x, double T, double gx, double gy, double P) { double[] v = new double[]{1, 0, 1}; double used = 0; for(int i = 0;i < T;i++){ used += x[i*2]*x[i*2] + x[i*2+1]*x[i*2+1]; double[][] M = { {1+V, -omega, x[i*2]}, {omega, 1+V, x[i*2+1]}, {0, 0, 1} }; v = mul(M, v); } // tr(used, P); // assert used <= P; tr(v, gx, gy); if(!(Point2D.distance(v[0], v[1], gx, gy) <= 1e-4))throw new RuntimeException(); } public static double[] solve(double[][] a, double[] c) { int n = a.length; int[] ps = new int[n]; for(int i = 0;i < n;i++)ps[i] = i; // Forward Elimination for(int i = 0;i < n;i++){ int pivot = -1; int from = -1; double amax = 0; for(int j = i;j < n;j++){ if(Math.abs(a[ps[j]][i]) > amax){ amax = Math.abs(a[ps[j]][i]); pivot = ps[j]; from = j; } } if(pivot == -1)return null; int d = ps[i]; ps[i] = ps[from]; ps[from] = d; for(int j = i+1;j < n;j++){ a[ps[i]][j] /= a[ps[i]][i]; } c[ps[i]] /= a[ps[i]][i]; a[ps[i]][i] = 1.0; for(int j = i+1;j < n;j++){ for(int k = i+1;k < n;k++){ a[ps[j]][k] -= a[ps[j]][i] * a[ps[i]][k]; } c[ps[j]] -= a[ps[j]][i] * c[ps[i]]; a[ps[j]][i] = 0.0; } } // Back Substitution for(int i = n-1;i >= 0;i--){ for(int j = i-1;j >= 0;j--){ c[ps[j]] -= a[ps[j]][i] * c[ps[i]]; } } double[] ret = new double[n]; for(int i = 0;i < n;i++){ ret[i] = c[ps[i]]; } return ret; } public static double[][] mul(double[][] A, double[][] B) { assert A[0].length == B.length; int m = A.length; int n = A[0].length; int o = B[0].length; double[][] C = new double[m][o]; for(int i = 0;i < m;i++){ for(int k = 0;k < n;k++){ for(int j = 0;j < o;j++){ C[i][j] += A[i][k] * B[k][j]; } } } return C; } public static double[] mul(double[][] A, double[] v) { int m = A.length; int n = v.length; double[] w = new double[m]; for(int i = 0;i < m;i++){ double sum = 0; for(int k = 0;k < n;k++){ sum += A[i][k] * v[k]; } w[i] = sum; } return w; } public static double[][] p2(double[][] A) { int n = A.length; double[][] C = new double[n][n]; for(int i = 0;i < n;i++){ for(int k = 0;k < n;k++){ for(int j = 0;j < n;j++){ C[i][j] += A[i][k] * A[k][j]; } } } return C; } // A^e*v public static double[] pow(double[][] A, double[] v, long m) { double[][] mu = A; double[] r = v; for(;m > 0;m>>>=1){ if((m&1)==1)r = mul(mu, r); mu = p2(mu); } return r; } void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } public static void main(String[] args) throws Exception { new N620_4().run(); } private byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[][] nmi(int n, int m) { int[][] map = new int[n][]; for(int i = 0;i < n;i++)map[i] = na(m); return map; } private int ni() { return (int)nl(); } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }