package q0xx; import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.InputMismatchException; public class Q22 { InputStream is; PrintWriter out; String INPUT = "4\r\n" + "10\r\n" + "100\r\n" + "1000000000\r\n" + "1000000000000000000"; void solve() { final int[] len = {1, 2, 10, 20, 100}; int[] offset = new int[6]; for(int i = 1;i <= 5;i++){ offset[i] = offset[i-1] + len[i-1]; } int n = offset[5]; int[][] M = new int[n+1][n+1]; for(int i = 0;i < 5;i++){ for(int j = 1;j < len[i];j++){ M[offset[i]+j][offset[i]+j-1] = 1; } M[offset[i]][offset[i]+len[i]-1] = 1; if(i < 4)M[offset[i+1]][offset[i]] = 1; } M[offset[5]][offset[4]] = 1; M[n][n] = 1; int[][][] Ms = new int[61][][]; Ms[0] = M; for(int i = 1;i <= 60;i++){ Ms[i] = p2(Ms[i-1]); } int[][][] nz = new int[61][][]; for(int i = 0;i <= 60;i++){ int p = 0; for(int j = 0;j <= n;j++){ for(int k = 0;k <= n;k++){ if(Ms[i][j][k] != 0){ p++; } } } nz[i] = new int[p][]; p = 0; for(int j = 0;j <= n;j++){ for(int k = 0;k <= n;k++){ if(Ms[i][j][k] != 0){ nz[i][p++] = new int[]{j, k, Ms[i][j][k]}; } } } } for(int T = ni();T >= 1;T--){ long m = nl()/5; int[] v = new int[n+1]; v[0] = 1; m += 5; for(int j = 0;m > 0;m>>>=1,j++){ if((m&1) == 1){ v = mulsparse(nz[j], v); } } out.println(v[n]); } } ///////// begin public static final int mod = 1000000009; public static final long m2 = (long)mod*mod; public static final long BIG = 8L*m2; // A^e*v public static int[] pow(int[][] A, int[] v, long e) { for(int i = 0;i < v.length;i++){ if(v[i] >= mod)v[i] %= mod; } int[][] MUL = A; for(;e > 0;e>>>=1) { if((e&1)==1)v = mul(MUL, v); MUL = p2(MUL); } return v; } // int matrix*int vector public static int[] mul(int[][] A, int[] v) { int m = A.length; int n = v.length; int[] w = new int[m]; for(int i = 0;i < m;i++){ long sum = 0; for(int k = 0;k < n;k++){ sum += (long)A[i][k] * v[k]; if(sum >= BIG)sum -= BIG; } w[i] = (int)(sum % mod); } return w; } public static int[] mulsparse(int[][] A, int[] v) { int m = A.length; int[] w = new int[m]; long sum = 0; for(int i = 0;i < A.length;i++){ sum += (long)A[i][2] * v[A[i][1]]; if(sum >= BIG)sum -= BIG; if(i+1 == A.length || A[i][0] != A[i+1][0]){ w[A[i][0]] = (int)(sum % mod); sum = 0; } } return w; } // int matrix^2 (be careful about negative value) public static int[][] p2(int[][] A) { int n = A.length; int[][] C = new int[n][n]; for(int i = 0;i < n;i++){ long[] sum = new long[n]; for(int k = 0;k < n;k++){ for(int j = 0;j < n;j++){ sum[j] += (long)A[i][k] * A[k][j]; if(sum[j] >= BIG)sum[j] -= BIG; } } for(int j = 0;j < n;j++){ C[i][j] = (int)(sum[j] % mod); } } return C; } //////////// end // A^e // O(N^3log N) public static int[][] pow(int[][] A, long e) { int[][] MUL = A; int n = A.length; int[][] C = new int[n][n]; for(int i = 0;i < n;i++)C[i][i] = 1; for(;e > 0;e>>>=1) { if((e&1)==1)C = mul(C, MUL); MUL = p2(MUL); } return C; } public static int[][] mul(int[][] A, int[][] B) { int m = A.length; int n = A[0].length; int o = B[0].length; int[][] C = new int[m][o]; for(int i = 0;i < m;i++){ long[] sum = new long[n]; for(int k = 0;k < n;k++){ for(int j = 0;j < n;j++){ sum[j] += (long)A[i][k] * B[k][j]; if(sum[j] >= BIG)sum[j] -= BIG; } } for(int j = 0;j < n;j++){ C[i][j] = (int)(sum[j] % mod); } } return C; } void run() throws Exception { // int n = 10000, m = 99999; // Random gen = new Random(); // StringBuilder sb = new StringBuilder(); // sb.append(n + " "); // for (int i = 0; i < n; i++) { // sb.append(Math.abs(gen.nextLong() % 1000000000000000000L) + " "); // } // INPUT = sb.toString(); 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"); } public static void main(String[] args) throws Exception { new Q22().run(); } private byte[] inbuf = new byte[1024]; private 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 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[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private int ni() { int num = 0, 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 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)); } }