import java.io.IOException; import java.io.InputStream; import java.io.OutputStream; import java.io.PrintStream; import java.io.PrintWriter; import java.lang.reflect.Array; import java.math.BigInteger; import java.util.ArrayDeque; import java.util.ArrayList; import java.util.Arrays; import java.util.Collection; import java.util.Collections; import java.util.Comparator; import java.util.HashMap; import java.util.List; import java.util.Map.Entry; import java.util.Map; import java.util.NoSuchElementException; import java.util.PriorityQueue; import java.util.Queue; import java.util.Random; import java.util.Set; import java.util.Stack; import java.util.TreeMap; import java.util.Vector; import java.util.function.BiFunction; import java.util.function.DoubleUnaryOperator; import java.util.function.IntFunction; import java.util.function.IntToDoubleFunction; import java.util.function.IntToLongFunction; import java.util.function.IntUnaryOperator; import java.util.function.LongToDoubleFunction; import java.util.function.Predicate; import java.util.function.ToIntFunction; import java.util.random.RandomGenerator; import java.util.stream.IntStream; import java.util.stream.LongStream; import java.util.stream.Stream; class BitVector { final int lg = 5; } class FastScanner { private static FastScanner instance = null; private final InputStream in = System.in; private final byte[] buffer = new byte[1024]; private int ptr = 0; private int buflen = 0; private FastScanner() { } public static FastScanner getInstance() { if (instance == null) { instance = new FastScanner(); } return instance; } private boolean hasNextByte() { if (ptr < buflen) { return true; } ptr = 0; try { buflen = in.read(buffer); } catch (IOException e) { e.printStackTrace(); } return buflen > 0; } private int readByte() { if (hasNextByte()) { return buffer[ptr++]; } else { return -1; } } private boolean isPrintableChar(int c) { return (33 <= c) && (c <= 126); } public boolean hasNext() { while (hasNextByte() && (!isPrintableChar(buffer[ptr]))) { ptr++; } return hasNextByte(); } public long nextLong() { if (!hasNext()) { throw new NoSuchElementException(); } long n = 0; boolean minus = false; int b = readByte(); if (b == '-') { minus = true; b = readByte(); } while ((b >= '0') && (b <= '9')) { // n = n * 10 + (b - '0'); n = ((n << 1) + (n << 3)) + (b - '0'); b = readByte(); } return minus ? -n : n; } public int nextInt() { return ((int) (nextLong())); } } class PolynomialFp { public static final long mod = 998244353; } /** * Fp[X1,X2,..]/(1-X1^1, 1-X2^2, ..) */ class InvolutivePolynomialFp { static final long mod = 998244353; } class ArrayUtils { public static void swap(long[] A, long[] B) { if (A.length != B.length) { throw new AssertionError(); } for (int i = 0; i < A.length; i++) { long tmp = A[i]; A[i] = B[i]; B[i] = tmp; } } } class MyPrintWriter extends PrintWriter { private static MyPrintWriter instance = null; private MyPrintWriter() { super(System.out); } public static MyPrintWriter getInstance() { if (instance == null) { instance = new MyPrintWriter(); } return instance; } public void println(boolean[][] a) { for (int i = 0; i < a.length; i++) { println(a[i], " "); } } public void println(boolean[] a, String separator) { for (int i = 0; i < a.length; ++i) { super.print((a[i] ? 1 : 0) + (i == (a.length - 1) ? "\n" : separator)); } } } class MathUtils { public static long gcd(long a, long b) { a = Math.abs(a); b = Math.abs(b); if (a == 0) { return b; } return MathUtils.gcd(b % a, a); } public static long modPow(long a, long n, long mod) { if (n < 0) { long inv = MathUtils.modInv(a, mod); return MathUtils.modPow(inv, -n, mod); } if (n == 0) { return 1; } return (MathUtils.modPow((a * a) % mod, n / 2, mod) * ((n % 2) == 1 ? a : 1)) % mod; } public static long pow(long a, long n) { if (n == 0) { return 1; } return MathUtils.pow(a * a, n / 2) * ((n % 2) == 1 ? a : 1); } /** * 拡張ユークリッドの互除法で逆元を求める。 * * @param a * @param mod * @return */ public static long modInv(long a, long mod) { a = ((a % mod) + mod) % mod; long[] f0 = new long[]{ 1, 0, mod }; long[] f1 = new long[]{ 0, 1, a }; while (f1[2] != 0) { long q = f0[2] / f1[2]; for (int i = 0; i < 3; i++) { f0[i] -= q * f1[i]; } ArrayUtils.swap(f0, f1); } return f0[1] < 0 ? mod + f0[1] : f0[1]; } /** * x=0のときはエラー * * @param x * @return */ public static int floorLog2(long x) { if (x == 0) { throw new AssertionError(); } return 63 - Long.numberOfLeadingZeros(x); } public static boolean isPrime(int mod) { if (mod == 2) { return true; } if ((mod == 1) || ((mod % 2) == 0)) { return false; } int[] testNumbers = new int[]{ 2, 7, 61 }; int pow2 = Integer.lowestOneBit(mod - 1); int log = MathUtils.floorLog2(pow2); for (int a : testNumbers) { a %= mod; if (a == 0) { continue; } long x = MathUtils.modPow(a, (mod - 1) / pow2, mod); if ((x == 1) || (x == (mod - 1))) { continue; } for (int i = 0; i < log; i++) { x = (x * x) % mod; if (x == (mod - 1)) { break; } if (i == (log - 1)) { return false; } } } return true; } static int findFactor(int n) { if (isPrime(n)) { return n; } if ((n % 2) == 0) { return 2; } Random rnd = new Random(); while (true) { long c = rnd.nextLong(1, n); long x = rnd.nextLong(1, n); long y = x; long d = 1; while ((d == 1) && (d != n)) { x = ((x * x) + c) % n; y = ((y * y) + c) % n; y = ((y * y) + c) % n; d = MathUtils.gcd(n, Math.abs(x - y)); if ((d != 1) && (d != n)) { return ((int) (d)); } } } } public static Map factor2(int n) { Map ret = new TreeMap<>(); for (long i = 2; (((1L * i) * i) <= n) && (i <= 1000); ++i) { int e = 0; while ((n % i) == 0) { n /= i; ++e; } if (e != 0) { ret.put(((int) (i)), e); } } Queue que = new ArrayDeque<>(); if (n != 1) { que.add(n); } while (!que.isEmpty()) { int m = que.poll(); int a = findFactor(m); if (m == a) { ret.merge(a, 1, Integer::sum); } else { que.add(a); que.add(m / a); } } return ret; } } public class Main implements Runnable { public static void main(String[] args) throws IOException { Thread.setDefaultUncaughtExceptionHandler((t, e) -> System.exit(1)); // new Main().gen(); // Runtime runtime = Runtime.getRuntime(); // new Thread(null, new Main(), "MainThreadWithLargeStack", (1024 * 1024) * 1024).start(); // new Main().test(); // new Main().gen(); new Main().run(); // new Main().solve(); // long usedMemory = runtime.totalMemory() - runtime.freeMemory(); // System.err.printf("使用メモリ: %.2f MB%n", usedMemory / 1024.0 / 1024.0); MyPrintWriter.getInstance().flush(); } @Override public void run() { FastScanner sc = FastScanner.getInstance(); MyPrintWriter pw = MyPrintWriter.getInstance(); int Q = sc.nextInt(); int[] m = new int[10000]; int[] r = new int[10000]; int msize = 0; int rsize = 0; Map> ermap = new HashMap<>(); int ng = 0; for (int q = 0; q < Q; q++) { int type = sc.nextInt(); if (type == 1) { if (ng > 0) { ng++; } int M = sc.nextInt(); int R = sc.nextInt(); int coprimeM = M; var factor = MathUtils.factor2(M); long res = 0; long fac = 1; for (int i = 0; i < msize; i++) { res = (res + (fac * r[i])) % M; fac = (fac * m[i]) % M; } long g = 1; int coprimeFac = ((int) (fac)); out : for (var es : factor.entrySet()) { int p = es.getKey().intValue(); int e = es.getValue().intValue(); int pe = ((int) (MathUtils.pow(p, e))); if (ermap.containsKey(es.getKey().intValue())) { int[] er2 = ermap.get(es.getKey().intValue()).peek(); int e2 = er2[0]; int r2 = er2[1]; int pe2 = ((int) (MathUtils.pow(p, e2))); if ((R % Math.min(pe, pe2)) != (r2 % Math.min(pe, pe2))) { if (ng == 0) { ng = 1; } } if (er2[0] >= e) { coprimeM /= pe; continue out; } g *= pe2; } else { ermap.put(es.getKey().intValue(), new Stack()); } ermap.get(es.getKey().intValue()).add(new int[]{ e, R % pe }); } coprimeFac %= coprimeM; long x = (((1L * (R - res)) / g) * MathUtils.modInv(coprimeFac / g, coprimeM / g)) % (coprimeM / g); coprimeM /= g; if (x < 0) { x += coprimeM; } m[msize++] = coprimeM; r[rsize++] = ((int) (x)); // res+fac*x==R mod M // fac*x=R-res mod M } else if (type == 2) { int k = sc.nextInt(); for (int i = 0; i < k; i++) { ng = Math.max(ng - 1, 0); var factor = MathUtils.factor2(m[msize - 1]); for (var es : factor.entrySet()) { var erque = ermap.get(es.getKey().intValue()); erque.pop(); if (erque.isEmpty()) { ermap.remove(es.getKey().intValue()); } } msize--; rsize--; } } else { long mod = sc.nextInt(); long ans = 0; long fac = 1; for (int i = 0; i < msize; i++) { ans += fac * r[i]; ans %= mod; fac = (fac * m[i]) % mod; } ans = ((ans % mod) + mod) % mod; pw.println(ng == 0 ? ans : -1); } } } }