package yukicoder_4950; import java.io.File; import java.io.FileInputStream; import java.io.FileNotFoundException; import java.io.IOException; import java.io.InputStream; import java.util.ArrayList; import java.util.BitSet; import java.util.NoSuchElementException; public class Main { public static void main(final String[] args) { new Main(); } public Main() { final InputChecker ic = new InputChecker(System.in); final java.io.PrintWriter out = new java.io.PrintWriter(System.out); solve(ic, out); out.flush(); } public void solve(final InputChecker ic, final java.io.PrintWriter out) { final int N = ic.nextInt(1, 100000); ic.nextChar(' '); final int P = ic.nextInt(223577, 223577); ic.readNewLine(); final int[] A = new int[N], B = new int[N]; { A[0] = ic.nextInt(0, P - 1); for (int i = 1;i < N;++ i) { ic.nextChar(' '); A[i] = ic.nextInt(0, P - 1); } ic.readNewLine(); B[0] = ic.nextInt(0, P - 1); for (int i = 1;i < N;++ i) { ic.nextChar(' '); B[i] = ic.nextInt(0, P - 1); } ic.readNewLine(); } ic.checkEOF(); { // 例外チェック boolean isZeroA = true, isZeroB = true; for (final int i : A) isZeroA &= i == 0; for (final int i : B) isZeroB &= i == 0; if (isZeroA) { if (isZeroB) { out.println(0); return; } out.println(-1); return; } if (isZeroB) { out.println(-1); return; } } if (N == 1) { int count = 0; for (;A[0] != B[0] && count < P;++ count) A[0] = add(A[0], A[0], P); if (A[0] == B[0]) { out.println(count + 1); while(count --> 0) out.println("1 1 1"); out.println(2); } else { out.println(-1); } return; } final ArrayList query = new ArrayList<>(); int base = 0; for (int i = 0;i < N;++ i) if (B[i] != 0) base = i; if (A[base] == 0) { for (int i = 0;i < N;++ i) { if (A[i] != 0) { query(base, i, P, A, query); break; } } } final int ADD1 = 1; final int ADD2 = ADD1 + 18; final int ADD3 = ADD2 + 512; final int ADD4 = ADD3 + 512; // 1~18: 0000,0001,0010,0100,... // 19~530: 0000,0010,1000,1010,... // 531~1042: 0000,0020,2000,2020,... if (N >= ADD2) { for (int i = 0;i < 18;++ i) { final int target = mod(1 << i, P); set1(add(base, i + ADD1, N), base, target, P, A, query); } } if (N >= ADD3) { for (int i = 0;i < 512;++ i) { final int target = mod(get4(i), P); set2(add(base, i + ADD2, N), base, target, P, A, query); } } if (N >= ADD4) { for (int i = 0;i < 512;++ i) { final int target = mul(2, get4(i), P); set3(add(base, i + ADD3, N), base, target, P, A, query); } } for (int i = N - 1;i >= ADD4;-- i) set4(add(base, i, N), base, B[add(base, i, N)], P, A, query); for (int i = Math.min(ADD4 - 1, N);i >= ADD3;-- i) set3(add(base, i, N), base, B[add(base, i, N)], P, A, query); for (int i = Math.min(ADD3 - 1, N);i >= ADD2;-- i) set2(add(base, i, N), base, B[add(base, i, N)], P, A, query); for (int i = Math.min(ADD2 - 1, N);i > 1;-- i) set1(add(base, i, N), base, B[add(base, i, N)], P, A, query); final int target = div(B[base], pow(2, 20, P), P); if (A[add(base, 1, N)] == 0) query(add(base, 1, N), base, P, A, query); set1(base, add(base, 1, N), target, P, A, query); set1(add(base, 1, N), base, B[add(base, 1, N)], P, A, query); while(A[base] != B[base]) query(base, base, P, A, query); // System.err.println(query.size() + 1); if (query.size() + 1 > P) throw new AssertionError(); for (int i = 0;i < N;++ i) if (A[i] != B[i]) throw new AssertionError(); out.println(query.size() + 1); for (final Query q : query) out.println(q); out.println(2); } // i番目の値を、j番目を利用してnに変える private static void set1(final int i, final int j, final int n, final int P, final int[] A, final ArrayList query) { final int diff = sub(n, A[i], P); int target = div(diff, A[j], P); while(target != 0) { if ((target & 1) != 0) query(i, j, P, A, query); query(j, j, P, A, query); target >>= 1; } } // 1~18を用いて変える private static void set2(final int i, final int base, final int n, final int P, final int[] A, final ArrayList query) { final int diff = sub(n, A[i], P); for (int j = 0;j < 18;++ j) { if ((diff >> j & 1) != 0) query(i, add(base, 1 + j, A.length), P, A, query); } } // 19~530を用いて変える private static void set3(final int i, final int base, final int n, final int P, final int[] A, final ArrayList query) { while(A[i] != n) { final int source = add(base + 19, get4_1(sub(n, A[i], P)), A.length); query(i, source, P, A, query); } } // 531~1042を用いて変える private static void set4(final int i, final int base, final int n, final int P, final int[] A, final ArrayList query) { final int source1 = add(base + 531, get4_2(sub(n, A[i], P)), A.length); query(i, source1, P, A, query); final int source2 = add(base + 19, get4_1(sub(n, A[i], P)), A.length); query(i, source2, P, A, query); } private static void query(final int i, final int j, final int P, final int[] A, final ArrayList query) { query.add(new Query(i, j)); A[i] = add(A[i], A[j], P); } private static int get4(final int n) { int ret = 0; for (int i = 0;i < 20;++ i) { if ((n >> i & 1) != 0) ret |= 1 << 2 * i; } return ret; } private static int get4_1(final int n) { int ret = 0; for (int i = 0;i < 15;++ i) { if ((n >> 2 * i & 3) != 0) ret |= 1 << i; } return ret; } private static int get4_2(final int n) { int ret = 0; for (int i = 0;i < 15;++ i) { if ((n >> 2 * i & 3) >= 2) ret |= 1 << i; } return ret; } private static class Query { final int i, j; /** A[i] += A[j] */ Query(final int i, final int j) { this.i = i; this.j = j; } @Override public String toString() { return "1 " + (i + 1) + " " + (j + 1); } } public static int mod(final int a, final int mod) { return a % mod; } public static int add(final int a, final int b, final int mod) { int ret = a + b; while (ret >= mod) ret -= mod; return ret; } public static int sub(final int a, final int b, final int mod) { int ret = a - b; while (ret < 0) ret += mod; return ret; } public static int mul(final int a, final int b, final int mod) { return (int)((long)a * b % mod); } public static int div(final int a,final int b, final int mod) { return mul(a, inv(b, mod), mod); } public static int inv(final int a, final int mod) { return pow(a, mod - 2, mod); } public static int pow(final int a, int b, final int mod) { int ans = 1; for (int mul = a;b > 0;b >>= 1, mul = mul(mul, mul, mod)) if ((b & 1) != 0) ans = mul(ans, mul, mod); return ans; } public static int exponent10(final int n, final int e) { return n * pow(10, e); } public static long exponent10L(final int n, final int e) { return n * pow(10L, e); } public static int pow(final int a, int b) { int ans = 1; for (int mul = a;b > 0;b >>= 1, mul *= mul) if ((b & 1) != 0) ans *= mul; return ans; } public static long pow(final long a, long b) { long ans = 1; for (long mul = a;b > 0;b >>= 1, mul *= mul) if ((b & 1) != 0) ans *= mul; return ans; } public static class CharSet { private final BitSet set = new BitSet(256); public void add(final char... c) { for (final char i : c) set.set(i); } public void add(final CharSet... s) { for (final CharSet i : s) set.or(i.set); } public boolean contains(final char... c) { for (final char i : c) if (!set.get(i)) return false; return true; } public boolean contains(final String s) { return contains(s.toCharArray()); } private static final class Chars extends CharSet { public Chars(final char... c) { super.add(c); } public Chars(final CharSet... s) { super.add(s); } @Override public void add(final char... c) { throw new UnsupportedOperationException(); } @Override public void add(final CharSet... s) { throw new UnsupportedOperationException(); } } public static final CharSet NUMBER = new Chars('0','1','2','3','4','5','6','7','8','9'); public static final CharSet LOWER = new Chars('a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z'); public static final CharSet UPPER = new Chars('A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','W','X','Y','Z'); public static final CharSet ALPHABET = new Chars(LOWER, UPPER); } public static class InputChecker { private InputStream in; private final byte[] buffer = new byte[1024]; private final byte[] undo = new byte[1024]; private int undoSize = 0; private int read = 0; private int length = 0; public InputChecker(final InputStream in) { this.in = in; } public final void setInputStream(final InputStream in) { this.in = in; } public final void setInputStream(final File in) { try { this.in = new FileInputStream(in); } catch (final FileNotFoundException e) { e.printStackTrace(); } } private boolean hasNextByte() { if (undoSize > 0) return true; if (read < length) return true; read = 0; try { length = in.read(buffer); } catch (final IOException e) { e.printStackTrace(); } return length > 0; } private byte readByte() { if (hasNextByte()) return undoSize > 0 ? undo[--undoSize] : buffer[read++]; throw new NoSuchElementException(); } private void undo(final byte b) { undo[undoSize ++] = b; } private void undo(final char c) { if ((c & 0xFF80) == 0) { undo((byte)c); return; } undo((byte)(c & 0x3F | 0x80)); if ((c & 0xF800) == 0) { undo((byte)(c >> 6 & 0x1F | 0xC0)); } else { undo((byte)(c >> 6 & 0x3F | 0x80)); undo((byte)(c >> 12 | 0xE0)); } } public final boolean hasNext() { return hasNextByte(); } public final char nextChar() { final byte b = readByte(); if ((b & 0x80) == 0) return (char)b; if ((b & 0x20) == 0) return (char)((b & 0x1F) << 6 | readByte() & 0x3F); return (char)((b & 0xF) << 12 | (readByte() & 0x3F) << 6 | readByte() & 0x3F); } public final char nextChar(final char estimate) { final char c = nextChar(); if (estimate == c) return estimate; undo(c); throw new AssertionError(); } public final char nextChar(final CharSet estimate) { final char c = nextChar(); if (estimate.contains(c)) return c; undo(c); throw new AssertionError(); } public final void readNewLine() { char c = nextChar(); if (c == '\r') { c = nextChar(); if (c != '\n') undo(c); return; } else if (c == '\n') return; undo(c); throw new AssertionError(); } public final void checkEOF() { if (hasNextByte()) throw new AssertionError(); } public final String next(final CharSet contains) { final StringBuilder sb = new StringBuilder(); try { do { final char c = nextChar(); if (!contains.contains(c)) { undo(c); return sb.toString(); } sb.append(c); } while(true); } catch (final NoSuchElementException e) { if (sb.length() <= 0) throw new AssertionError(); return sb.toString(); } } public final int nextInt() { byte b = readByte(); int n = 0; if (b == '-') { if (!isNumber(b = readByte())) { undo(b); throw new NumberFormatException(); } try { if (b == '0') { if (!isNumber(b = readByte())) { undo(b); return 0; } throw new NumberFormatException(); } do n = Math.addExact(Math.multiplyExact(n, 10), '0' - b); while(isNumber(b = readByte())); undo(b); } catch (final NoSuchElementException e) { } return n; } if (!isNumber(b)) { undo(b); throw new NumberFormatException(); } try { if (b == '0') { if (!isNumber(b = readByte())) { undo(b); return 0; } throw new NumberFormatException(); } do n = Math.addExact(Math.multiplyExact(n, 10), b - '0'); while(isNumber(b = readByte())); undo(b); } catch (final NoSuchElementException e) { } return n; } public final int nextInt(final int min, final int max) { final int n = nextInt(); if (min <= n && n <= max) return n; throw new NumberFormatException(); } private static boolean isNumber(final byte c) { return '0' <= c && c <= '9'; } public final long nextLong() { byte b = readByte(); long n = 0; if (b == '-') { if (!isNumber(b = readByte())) { undo(b); throw new NumberFormatException(); } try { if (b == '0') { if (!isNumber(b = readByte())) { undo(b); return 0; } throw new NumberFormatException(); } do n = Math.addExact(Math.multiplyExact(n, 10), '0' - b); while(isNumber(b = readByte())); undo(b); } catch (final NoSuchElementException e) { } return n; } if (!isNumber(b)) { undo(b); throw new NumberFormatException(); } try { if (b == '0') { if (!isNumber(b = readByte())) { undo(b); return 0; } throw new NumberFormatException(); } do n = Math.addExact(Math.multiplyExact(n, 10), b - '0'); while(isNumber(b = readByte())); undo(b); } catch (final NoSuchElementException e) { } return n; } public final long nextLong(final long min, final long max) { final long n = nextLong(); if (min <= n && n <= max) return n; throw new NumberFormatException(); } public final double nextDouble() { final StringBuilder sb = new StringBuilder(); byte b = readByte(); if (b == '-') { sb.append(b); b = readByte(); } if (b == '0') { sb.append(b); b = readByte(); } else { while(isNumber(b)) { sb.append(b); b = readByte(); } } if (b == '.') { sb.append(b); b = readByte(); while(isNumber(b)) { sb.append(b); b = readByte(); } } if (b == 'e' || b == 'E') { sb.append(b); b = readByte(); if (b == '-' || b == '+') { sb.append(b); b = readByte(); } while(isNumber(b)) { sb.append(b); b = readByte(); } } undo(b); return Double.parseDouble(sb.toString()); } } }