Submission #3071118

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Source Code Expand

// package other2015.utpc2014;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.Map;

public class Main {
    static long __startTime = System.currentTimeMillis();

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        long a = in.nextLong();
        long b = in.nextLong();
        long x = in.nextLong();
        if (a == x) {
            out.println(0);
            out.flush();
            return;
        }

        int step = 1<<18;
        long[] smallStep = new long[step];
        smallStep[0] = x<<20;

        {
            long last = x;
            for (int i = 1; i < step; i++) {
                last = nextNaive(last, b);
                smallStep[i] = (last<<20)|i;
            }
        }
        Arrays.sort(smallStep);

        final long MASK = (1<<20)-1;
        long[] mat2 = generateMat2(b);
        long[] matGiantStep = MatrixMod2.pow(mat2, 1<<18);

        {
            long last = a;
            for (long n = step ; n <= (1L << 36); n += step) {
                long next = MatrixMod2.mul(matGiantStep, last);
                long from = next<<20;
                int fi = Arrays.binarySearch(smallStep, from);
                if (fi < 0) {
                    fi = -fi-1;
                }

                if (fi < smallStep.length && (smallStep[fi]>>20) == next) {
                    long to = (next+1)<<20;
                    long toIdx = Long.MIN_VALUE;
                    long fromIdx = Long.MAX_VALUE;

                    while (fi < smallStep.length && smallStep[fi] < to) {
                        long idx = n - (smallStep[fi]&MASK);
                        fromIdx = Math.min(fromIdx, idx);
                        toIdx = Math.max(toIdx, idx);
                        fi++;
                    }

                    long iter = MatrixMod2.mul(MatrixMod2.pow(mat2, fromIdx), a);
                    while (fromIdx <= toIdx) {
                        if (iter == x) {
                            out.println(fromIdx);
                            out.flush();
                            return;
                        }
                        iter = nextNaive(iter, b);
                        fromIdx++;
                    }
                    break;
                }
                last = next;
            }
        }
        out.println(-1);
        out.flush();
    }

    private static boolean verify(long[] mat2, long a, long x) {
        return MatrixMod2.mul(mat2, a) == x;
    }

    static long[] generateMat2(long b) {
        long[] matA = new long[40];
        for (int i = 0; i < 35 ; i++) {
            matA[i] = 1L<<(i+1);
        }
        long[] matB = new long[40];
        for (int i = 0; i < 36; i++) {
            matB[i] = 1L<<i;
        }
        matB[39] = 1;

        long[] matC = new long[40];
        for (int i = 0; i < 40 ; i++) {
            long has = (b & (1L<<i)) >= 1 ? 1 : 0;
            matC[i] = has<<39;
        }
        return MatrixMod2.add(matA, MatrixMod2.mul(matC, matB));
    }

    static long nextNaive(long a, long b) {
        return (a / 2) ^ ((a % 2) * b);
    }

    public static class MatrixMod2 {
        static long[] e(int n) {
            long[] mat = new long[n];
            for (int i = 0; i < n ; i++) {
                mat[i] = 1L<<i;
            }
            return mat;
        }

        static long[] add(long[] a, long[] b) {
            long[] c = new long[a.length];
            for (int i = 0; i < c.length; i++) {
                c[i] = a[i] ^ b[i];
            }
            return c;
        }

        static long[] flip(long[] a) {
            long[] r = new long[a.length];
            for (int i = 0; i < a.length ; i++) {
                for (int j = 0; j < a.length ; j++) {
                    r[j] |= ((a[i]&(1L<<j))>>j)<<i;
                }
            }
            return r;
        }

        static long[] mul(long[] a, long[] b) {
            long[] res = new long[a.length];
            long[] r = flip(b);
            for (int i = 0; i < a.length ; i++) {
                for (int j = 0; j < a.length; j++) {
                    long c = Long.bitCount(a[i] & r[j]) % 2;
                    res[i] |= c<<j;
                }
            }
            return res;
        }

        static long mul(long[] a, long b) {
            long r = 0;
            for (int i = 0; i < a.length; i++) {
                long c = Long.bitCount(a[i] & b) % 2;
                r |= c<<i;
            }
            return r;
        }

        static long[] pow(long[] x, long p) {
            int n = x.length;
            long[] ret = e(n);
            while (p >= 1) {
                if ((p & 1) == 1) {
                    ret = mul(ret, x);
                }
                x = mul(x, x);
                p >>>= 1;
            }
            return ret;
        }
    }

    private static void printTime(String label) {
        debug(label, System.currentTimeMillis() - __startTime);
    }

    private static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }

    public static class InputReader {
        private static final int BUFFER_LENGTH = 1 << 12;
        private InputStream stream;
        private byte[] buf = new byte[BUFFER_LENGTH];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int next() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public char nextChar() {
            return (char) skipWhileSpace();
        }

        public String nextToken() {
            int c = skipWhileSpace();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInt() {
            return (int) nextLong();
        }

        public long nextLong() {
            int c = skipWhileSpace();
            long sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = next();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            return Double.valueOf(nextToken());
        }

        int skipWhileSpace() {
            int c = next();
            while (isSpaceChar(c)) {
                c = next();
            }
            return c;
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}

Submission Info

Judge Result