Problem: And now the numerous qualifying tournaments for one of the most prestigious Russian contests Russian Codec Cup are over. All n participants who have made it to the finals found themselves in a huge m-floored 108-star hotel. Of course the first thought to come in a place like this is "How about checking out the elevator?".

The hotel's elevator moves between floors according to one never changing scheme. Initially (at the moment of time 0) the elevator is located on the 1-st floor, then it moves to the 2-nd floor, then — to the 3-rd floor and so on until it reaches the m-th floor. After that the elevator moves to floor m - 1, then to floor m - 2, and so on until it reaches the first floor. This process is repeated infinitely. We know that the elevator has infinite capacity; we also know that on every floor people get on the elevator immediately. Moving between the floors takes a unit of time.

For each of the n participant you are given si, which represents the floor where the i-th participant starts, fi, which represents the floor the i-th participant wants to reach, and ti, which represents the time when the i-th participant starts on the floor si.

For each participant print the minimum time of his/her arrival to the floor fi. 

If the elevator stops on the floor si at the time ti, then the i-th participant can enter the elevator immediately. If the participant starts on the floor si and that's the floor he wanted to reach initially (si = fi), then the time of arrival to the floor fi for this participant is considered equal to ti.

Input

The first line contains two space-separated integers n and m (1 ≤ n ≤ 105, 2 ≤ m ≤ 108). 

Next n lines contain information about the participants in the form of three space-separated integers si fi ti (1 ≤ si, fi ≤ m, 0 ≤ ti ≤ 108), described in the problem statement.

Output

Print n lines each containing one integer — the time of the arrival for each participant to the required floor.

Examples

Input

7 4
2 4 3
1 2 0
2 2 0
1 2 1
4 3 5
1 2 2
4 2 0


Output

9
1
0
7
10
7
5


Input

5 5
1 5 4
1 3 1
1 3 4
3 1 5
4 2 5


Output

12
10
10
8
7

Note

Let's consider the first sample. The first participant starts at floor s = 2 by the time equal to t = 3. To get to the floor f = 4, he has to wait until the time equals 7, that's the time when the elevator will go upwards for the second time. Then the first participant should get on the elevator and go two floors up. In this case the first participant gets to the floor f at time equal to 9. The second participant starts at the time t = 0 on the floor s = 1, enters the elevator immediately, and arrives to the floor f = 2. The third participant doesn't wait for the elevator, because he needs to arrive to the same floor where he starts.

Solution (in JAVA):

Solution:
import static java.lang.Math.*;
import java.util.*;
import java.io.*;

public class A {

    public void solve() throws Exception {

        long n = nextInt(), m = nextInt();
        long period = (m-1)*2;
        debug(period);
        for (int i=0; i<n; ++i) {
            long s = nextInt(), f = nextInt(), t = nextInt();
            long x, y;
            if (s==f) println(t);
            else if (s<f) {
                x = (t/period)*period + s-1;
//              debug("x",x);
                while (x<t) x+= period;
//              debug(x);
                println(x + f-s);
            }
            else {
                x = (t/period)*period + m-1 + m-s;
//              debug("x",x);
                while (x<t) x+=period;
//              debug(x);
                println(x + s-f);
            }
        }

    }



    ////////////////////////////////////////////////////////////////////////////

    boolean showDebug = true;

    double EPS = 1e-7;
    int INF = Integer.MAX_VALUE;
    long INFL = Long.MAX_VALUE;
    double INFD = Double.MAX_VALUE;


    int absPos(int num) {
        return num<0 ? 0:num;
    }
    long absPos(long num) {
        return num<0 ? 0:num;
    }
    double absPos(double num) {
        return num<0 ? 0:num;
    }

    int min(int... nums) {
        int r = INF;
        for (int i: nums)
            if (i<r) r=i;
        return r;
    }
    int max(int... nums) {
        int r = -INF;
        for (int i: nums)
            if (i>r) r=i;
        return r;
    }
    long minL(long... nums) {
        long r = INFL;
        for (long i: nums)
            if (i<r) r=i;
        return r;
    }
    long maxL(long... nums) {
        long r = -INFL;
        for (long i: nums)
            if (i>r) r=i;
        return r;
    }
    double minD(double... nums) {
        double r = INFD;
        for (double i: nums)
            if (i<r) r=i;
        return r;
    }
    double maxD(double... nums) {
        double r = -INFD;
        for (double i: nums)
            if (i>r) r=i;
        return r;
    }

    long sumArr(int[] arr) {
        long res = 0;
        for (int i: arr)
            res+=i;
        return res;
    }
    long sumArr(long[] arr) {
        long res = 0;
        for (long i: arr)
            res+=i;
        return res;
    }
    double sumArr(double[] arr) {
        double res = 0;
        for (double i: arr)
            res+=i;
        return res;
    }

    long partsFitCnt(long partSize, long wholeSize) {
        return (partSize+wholeSize-1)/partSize;
    }

    boolean odd(long num) {
        return (num&1)==1;
    }

    boolean hasBit(int num, int pos) {
        return (num&(1<<pos))>0;
    }

    long binpow(int a, int n) {
        long r = 1;
        while (n>0) {
            if ((n&1)!=0) r*=a;
            a*=a;
            n>>=1;
        }
        return r;
    }

    boolean isLetter(char c) {
        return (c>='a' && c<='z') || (c>='A' && c<='Z');
    }
    boolean isLowercase(char c) {
        return (c>='a' && c<='z');
    }
    boolean isUppercase(char c) {
        return (c>='A' && c<='Z');
    }
    boolean isDigit(char c) {
        return (c>='0' && c<='9');
    }

    String stringn(String s, int n) {
        if (n<1) return "";
        StringBuilder sb = new StringBuilder(s.length()*n);
        for (int i=0; i<n; ++i) sb.append(s);
        return sb.toString();
    }
    String str(Object o) {
        return o.toString();
    }


    long timer = System.currentTimeMillis();
    void startTimer() {
        timer = System.currentTimeMillis();
    }
    void stopTimer() {
        System.err.println("time: "+(System.currentTimeMillis()-timer)/1000.0);
    }


    class InputReader {
        private byte[] buf;
        private int bufPos = 0, bufLim = -1;
        public InputReader(int size) {
            buf = new byte[size];
        }
        private void fillBuf() throws IOException {
            bufLim = System.in.read(buf);
            bufPos = 0;
        }
        char read() throws IOException {
            if (bufPos>=bufLim) fillBuf(); 
            return (char)buf[bufPos++];
        }
        boolean hasInput() throws IOException {
            if (bufPos>=bufLim) fillBuf();
            return bufPos<bufLim;
        }
    }

    InputReader inputReader = new InputReader(1<<16);
    static BufferedWriter outputWriter = new BufferedWriter(new OutputStreamWriter(System.out), 1<<16);

    char nextChar() throws IOException {
        return inputReader.read();
    }
    char nextNonWhitespaceChar() throws IOException {
        char c = inputReader.read();
        while (c<=' ') c=inputReader.read();
        return c;
    }
    String nextWord() throws IOException {
        StringBuilder sb = new StringBuilder();
        char c = inputReader.read();
        while (c<=' ') c=inputReader.read();
        while (c>' ') {
            sb.append(c);
            c = inputReader.read();
        }
        return new String(sb);
    }
    String nextLine() throws IOException {
        StringBuilder sb = new StringBuilder();
        char c = inputReader.read();
        while (c<=' ') c=inputReader.read();
        while (c!='\n' && c!='\r') {
            sb.append(c);
            c = inputReader.read();
        }
        return new String(sb);
    }
    int nextInt() throws IOException {
        int r = 0;
        char c = nextNonWhitespaceChar();
        boolean neg = false;
        if (c=='-') neg=true;
        else r=c-48;
        c = nextChar();
        while (c>='0' && c<='9') {
            r*=10;
            r+=c-48;
            c=nextChar();
        }
        return neg ? -r:r;
    }
    long nextLong() throws IOException {
        long r = 0;
        char c = nextNonWhitespaceChar();
        boolean neg = false;
        if (c=='-') neg=true;
        else r = c-48;
        c = nextChar();
        while (c>='0' && c<='9') {
            r*=10L;
            r+=c-48L;
            c=nextChar();
        }
        return neg ? -r:r;
    }
    double nextDouble() throws NumberFormatException, IOException {
        return Double.parseDouble(nextWord());
    }
    int[] nextArr(int size) throws NumberFormatException, IOException {
        int[] arr = new int[size];
        for (int i=0; i<size; ++i)
            arr[i] = nextInt();
        return arr;
    }
    long[] nextArrL(int size) throws NumberFormatException, IOException {
        long[] arr = new long[size];
        for (int i=0; i<size; ++i)
            arr[i] = nextLong();
        return arr;
    }
    double[] nextArrD(int size) throws NumberFormatException, IOException {
        double[] arr = new double[size];
        for (int i=0; i<size; ++i)
            arr[i] = nextDouble();
        return arr;
    }
    String[] nextArrS(int size) throws NumberFormatException, IOException {
        String[] arr = new String[size];
        for (int i=0; i<size; ++i)
            arr[i] = nextWord();
        return arr;
    }
    char[] nextArrCh(int size) throws IOException {
        char[] arr = new char[size];
        for (int i=0; i<size; ++i)
            arr[i] = nextNonWhitespaceChar();
        return arr;
    }
    char[][] nextArrCh(int rows, int columns) throws IOException {
        char[][] arr = new char[rows][columns];
        for (int i=0; i<rows; ++i)
            for (int j=0; j<columns; ++j)
                arr[i][j] = nextNonWhitespaceChar();
        return arr;
    }
    char[][] nextArrChBorders(int rows, int columns, char border) throws IOException {
        char[][] arr = new char[rows+2][columns+2];
        for (int i=1; i<=rows; ++i)
            for (int j=1; j<=columns; ++j)
                arr[i][j] = nextNonWhitespaceChar();
        for (int i=0; i<columns+2; ++i) {
            arr[0][i] = border;
            arr[rows+1][i] = border;
        }
        for (int i=0; i<rows+2; ++i) {
            arr[i][0] = border;
            arr[i][columns+1] = border;
        }
        return arr;
    }

    void printf(String format, Object... args) throws IOException {
        outputWriter.write(String.format(format, args));
    }
    void print(Object o) throws IOException {
        outputWriter.write(o.toString());
    }
    void println(Object o) throws IOException {
        outputWriter.write(o.toString());
        outputWriter.newLine();
    }
    void print(Object... o) throws IOException {
        for (int i=0; i<o.length; ++i) {
            if (i!=0) outputWriter.write(' ');
            outputWriter.write(o[i].toString());
        }
    }
    void println(Object... o) throws IOException {
        print(o);
        outputWriter.newLine();
    }
    void printn(Object o, int n) throws IOException {
        String s = o.toString();
        for (int i=0; i<n; ++i) {
            outputWriter.write(s);
            if (i!=n-1) outputWriter.write(' ');
        }
    }
    void printnln(Object o, int n) throws IOException {
        printn(o, n);
        outputWriter.newLine();
    }
    void printArr(int[] arr) throws IOException {
        for (int i=0; i<arr.length; ++i) {
            if (i!=0) outputWriter.write(' ');
            outputWriter.write(Integer.toString(arr[i]));
        }
    }
    void printArr(long[] arr) throws IOException {
        for (int i=0; i<arr.length; ++i) {
            if (i!=0) outputWriter.write(' ');
            outputWriter.write(Long.toString(arr[i]));
        }
    }
    void printArr(double[] arr) throws IOException {
        for (int i=0; i<arr.length; ++i) {
            if (i!=0) outputWriter.write(' ');
            outputWriter.write(Double.toString(arr[i]));
        }
    }
    void printArr(String[] arr) throws IOException {
        for (int i=0; i<arr.length; ++i) {
            if (i!=0) outputWriter.write(' ');
            outputWriter.write(arr[i]);
        }
    }
    void printArr(char[] arr) throws IOException {
        for (char c: arr) outputWriter.write(c);
    }
    void printlnArr(int[] arr) throws IOException {
        printArr(arr);
        outputWriter.newLine();
    }
    void printlnArr(long[] arr) throws IOException {
        printArr(arr);
        outputWriter.newLine();
    }
    void printlnArr(double[] arr) throws IOException {
        printArr(arr);
        outputWriter.newLine();
    }
    void printlnArr(String[] arr) throws IOException {
        printArr(arr);
        outputWriter.newLine();
    }
    void printlnArr(char[] arr) throws IOException {
        printArr(arr);
        outputWriter.newLine();
    }

    void debug(Object... o) {
        if (showDebug) System.err.println(Arrays.deepToString(o));
    }


    public static void main(String[] args) throws Exception {
        Locale.setDefault(Locale.US);
        new A().solve();
        outputWriter.flush(); outputWriter.close();
    }
}