Problem: Vasya the Great Magician and Conjurer loves all kinds of miracles and wizardry. In one wave of a magic wand he can turn an object into something else. But, as you all know, there is no better magic in the Universe than the magic of numbers. That's why Vasya adores math and spends a lot of time turning some numbers into some other ones.

This morning he has n cards with integers lined up in front of him. Each integer is not less than 1, but not greater than l. When Vasya waves his magic wand, two rightmost cards vanish from the line and a new card magically appears in their place. It contains the difference between the left and the right numbers on the two vanished cards. Vasya was very interested to know what would happen next, and so he waved with his magic wand on and on, until the table had a single card left.

Suppose that Vasya originally had the following cards: 4, 1, 1, 3 (listed from left to right). Then after the first wave the line would be: 4, 1, -2, and after the second one: 4, 3, and after the third one the table would have a single card with number 1.

Please note that in spite of the fact that initially all the numbers on the cards were not less than 1 and not greater than l, the numbers on the appearing cards can be anything, no restrictions are imposed on them.

It is now evening. Vasya is very tired and wants to return everything back, but does not remember which cards he had in the morning. He only remembers that there were n cards, they contained integers from 1 to l, and after all magical actions he was left with a single card containing number d.

Help Vasya to recover the initial set of cards with numbers.

Input

The single line contains three space-separated integers: n (2 ≤ n ≤ 100) — the initial number of cards on the table, d (|d| ≤ 104) — the number on the card that was left on the table after all the magical actions, and l (1 ≤ l ≤ 100) — the limits for the initial integers.

Output

If Vasya is mistaken, that is, if there doesn't exist a set that meets the requirements given in the statement, then print a single number -1, otherwise print the sought set containing n integers from 1 to l. Separate the integers by spaces. Print the integers in the order, in which they were written on the cards from left to right. If there are several suitable sets of numbers, you can print any of them.

Examples

Input

3 3 2


Output

2 1 2 

Input

5 -4 3


Output

-1


Input

5 -4 4


Output

2 4 1 4 1 

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.util.Map.*;
import java.math.*;

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        Task solver = new B();
        solver.solve(1, in, out);
        out.close();
    }
}

interface Task {
    public void solve(int testNumber, InputReader in, OutputWriter out);
}

class A implements Task {
    
    public void solve(int testNumber, InputReader in, OutputWriter out){
        int n=in.readInt(), x, ret=0;
        while (n-->0) {
        	x=in.readInt()+in.readInt()+in.readInt();
        	if (x>=2) ret++;
        }
        out.printLine(ret);
    }
    
    boolean isVowel(char c) {
        return c=='a' || c=='e' || c=='i' || c=='o' || c=='u' || c=='y' || c=='A' || c=='E' || c=='I' || c=='O' || c=='U' || c=='Y';
    }
    
}

class B implements Task {
    
    int[] arr;
    
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        int n=in.readInt(), d=in.readInt(), l=in.readInt(), ret=-1, x;
        arr=new int[n];
        for (int i=0; i<n; i++) arr[i]=1;
        if (n%2==1) d--;
        if (d>0) for (int i=0; i<n; i+=2) {
        	x=Math.min(d, l-1);
        	arr[i]+=x;
        	d-=x;
        }
        else for (int i=1; i<n; i+=2) {
        	x=Math.min(-d, l-1);
        	arr[i]+=x;
        	d+=x;
        }
        if (d!=0) out.printLine(-1);
        else out.printLine(arr);
    }
    
    int f1(StringBuilder str) {
        int ret=0;
        for (int i=0; i<str.length(); i++) ret=26*ret+str.charAt(i)-'A'+1;
        return ret;
    }
    
    String f2(int n) {
        StringBuilder ret=new StringBuilder();
        for (; n>0; n/=26) {
            n--;
            ret.insert(0, (char)('A'+n%26));
            //System.out.println(n+" "+('A'+n%26));
        }
        return ret.toString();
    }
    
}

class C implements Task {
    
    int dx[]={-1, 0, 0, 1}, dy[]={0, -1, 1, 0};
    Set<Point> pontos=new TreeSet<Point>();
    Point[] points;
    
    public void solve(int testNumber, InputReader in, OutputWriter out){
        int n=in.readInt(), x, y;
        while (n-->0) {
            x=in.readInt();
            y=in.readInt();
            for (int i=0; i<4; i++) pontos.add(new Point(x+dx[i], y+dy[i]));
        }
        points=pontos.toArray(new Point[pontos.size()]);
        Polygon poligono=Polygon.convexHull(pontos.toArray(points));
        int ret=0;
        for (int i=0; i<poligono.vertices.length; i++) {
            int j=(i+1)%poligono.vertices.length, x1=(int)(poligono.vertices[i].x), x2=(int)(poligono.vertices[j].x),
                    y1=(int)(poligono.vertices[i].y), y2=(int)(poligono.vertices[j].y);
            ret+=Math.max(Math.abs(x1-x2), Math.abs(y1-y2));
            //out.printLine(poligono.vertices[i]);
        }
        out.printLine(ret);
    }
    
    double cross(Vector v0, Vector v1) {
        return Math.abs(v0.x*v1.y-v0.y*v1.x);
    }
    
    double gcd(double a, double b) {
        if (Math.abs(b)<GeometryUtils.epsilon) return a;
        return gcd(b, a%b);
    }
    
}

class Polygon {
    public final Point[] vertices;
    private Segment[] sides;

    public Polygon(Point...vertices) {
        this.vertices = vertices.clone();
    }

    public double square() {
        double sum = 0;
        for (int i = 1; i < vertices.length; i++)
            sum += (vertices[i].x - vertices[i - 1].x) * (vertices[i].y + vertices[i - 1].y);
        sum += (vertices[0].x - vertices[vertices.length - 1].x) * (vertices[0].y + vertices[vertices.length - 1].y);
        return Math.abs(sum) / 2;
    }

    public Point center() {
        double sx = 0;
        double sy = 0;
        for (Point point : vertices) {
            sx += point.x;
            sy += point.y;
        }
        return new Point(sx / vertices.length, sy / vertices.length);
    }

    public static boolean over(Point a, Point b, Point c) {
        return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y) < -GeometryUtils.epsilon;
    }

    private static boolean under(Point a, Point b, Point c) {
        return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y) > GeometryUtils.epsilon;
    }

    public static Polygon convexHull(Point[] points) {
        if (points.length == 1)
            return new Polygon(points);
        Arrays.sort(points);
        Point left = points[0];
        Point right = points[points.length - 1];
        List<Point> up = new ArrayList<Point>();
        List<Point> down = new ArrayList<Point>();
        for (Point point : points) {
            if (point == left || point == right || !under(left, point, right)) {
                while (up.size() >= 2 && under(up.get(up.size() - 2), up.get(up.size() - 1), point))
                    up.remove(up.size() - 1);
                up.add(point);
            }
            if (point == left || point == right || !over(left, point, right)) {
                while (down.size() >= 2 && over(down.get(down.size() - 2), down.get(down.size() - 1), point))
                    down.remove(down.size() - 1);
                down.add(point);
            }
        }
        Point[] result = new Point[up.size() + down.size() - 2];
        int index = 0;
        for (Point point : up)
            result[index++] = point;
        for (int i = down.size() - 2; i > 0; i--)
            result[index++] = down.get(i);
        return new Polygon(result);
    }

    public boolean contains(Point point) {
        return contains(point, false);
    }

    public boolean contains(Point point, boolean strict) {
        for (Segment segment : sides()) {
            if (segment.contains(point, true))
                return !strict;
        }
        double totalAngle = GeometryUtils.canonicalAngle(Math.atan2(vertices[0].y - point.y, vertices[0].x - point.x) -
            Math.atan2(vertices[vertices.length - 1].y - point.y, vertices[vertices.length - 1].x - point.x));
        for (int i = 1; i < vertices.length; i++) {
            totalAngle += GeometryUtils.canonicalAngle(Math.atan2(vertices[i].y - point.y, vertices[i].x - point.x) -
                Math.atan2(vertices[i - 1].y - point.y, vertices[i - 1].x - point.x));
        }
        return Math.abs(totalAngle) > Math.PI;
    }

    public Segment[] sides() {
        if (sides == null) {
            sides = new Segment[vertices.length];
            for (int i = 0; i < vertices.length - 1; i++)
                sides[i] = new Segment(vertices[i], vertices[i + 1]);
            sides[sides.length - 1] = new Segment(vertices[vertices.length - 1], vertices[0]);
        }
        return sides;
    }

    public static double triangleSquare(Point a, Point b, Point c) {
        return Math.abs((a.x - b.x) * (a.y + b.y) + (b.x - c.x) * (b.y + c.y) + (c.x - a.x) * (c.y + a.y)) / 2;
    }

    public double perimeter() {
        double result = vertices[0].distance(vertices[vertices.length - 1]);
        for (int i = 1; i < vertices.length; i++)
            result += vertices[i].distance(vertices[i - 1]);
        return result;
    }
}

class Segment {
    public final Point a;
    public final Point b;
    private double distance = Double.NaN;
    private Line line = null;

    public Segment(Point a, Point b) {
        this.a = a;
        this.b = b;
    }

    public double length() {
        if (Double.isNaN(distance))
            distance = a.distance(b);
        return distance;
    }

    public double distance(Point point) {
        double length = length();
        double left = point.distance(a);
        if (length < GeometryUtils.epsilon)
            return left;
        double right = point.distance(b);
        if (left * left > right * right + length * length)
            return right;
        if (right * right > left * left + length * length)
            return left;
        return point.distance(line());
    }

    public Point intersect(Segment other, boolean includeEnds) {
        Line line = line();
        Line otherLine = other.a.line(other.b);
        if (line.parallel(otherLine))
            return null;
        Point intersection = line.intersect(otherLine);
        if (contains(intersection, includeEnds) && other.contains(intersection, includeEnds))
            return intersection;
        else
            return null;
    }

    public boolean contains(Point point, boolean includeEnds) {
        if (a.equals(point) || b.equals(point))
            return includeEnds;
        if (a.equals(b))
            return false;
        Line line = line();
        if (!line.contains(point))
            return false;
        Line perpendicular = line.perpendicular(a);
        double aValue = perpendicular.value(a);
        double bValue = perpendicular.value(b);
        double pointValue = perpendicular.value(point);
        return aValue < pointValue && pointValue < bValue || bValue < pointValue && pointValue < aValue;
    }

    public Line line() {
        if (line == null)
            line = a.line(b);
        return line;
    }

    public Point middle() {
        return new Point((a.x + b.x) / 2, (a.y + b.y) / 2);
    }

    public Point[] intersect(Circle circle) {
        Point[] result = line().intersect(circle);
        if (result.length == 0)
            return result;
        if (result.length == 1) {
            if (contains(result[0], true))
                return result;
            return new Point[0];
        }
        if (contains(result[0], true)) {
            if (contains(result[1], true))
                return result;
            return new Point[]{result[0]};
        }
        if (contains(result[1], true))
            return new Point[]{result[1]};
        return new Point[0];
    }

    public Point intersect(Line line) {
        Line selfLine = line();
        Point intersect = selfLine.intersect(line);
        if (intersect == null)
            return null;
        if (contains(intersect, true))
            return intersect;
        return null;
    }

    public double distance(Segment other) {
        Line line = line();
        Line otherLine = other.line();
        Point p = line == null || otherLine == null ? null : line.intersect(otherLine);
        if (p != null && contains(p, true) && other.contains(p, true))
            return 0;
        return Math.min(Math.min(other.distance(a), other.distance(b)), Math.min(distance(other.a), distance(other.b)));
    }
}

class Vector {
    public final double x;
    public final double y;
    public final Point point;

    public Vector(double x, double y) {
            this.x = x;
            this.y = y;
            point = new Point(x, y);
    }

    public Vector(Point point) {
            this.x = point.x;
            this.y = point.y;
            this.point = point;
    }

    public Vector(Point from, Point to) {
            this(to.x - from.x, to.y - from.y);
    }

    public double angleTo(Vector other) {
            return GeometryUtils.canonicalAngle(other.point.angle() - point.angle());
    }

    public double length() {
            return point.value();
    }

    public double angle() {
            return point.angle();
    }
}

class Point implements Comparable<Point>{
    public static final Point ORIGIN = new Point(0, 0);
    public final double x;
    public final double y;
    
    public int compareTo(Point o2) {
        int value = Double.compare(this.x, o2.x);
        if (value != 0)
            return value;
        return Double.compare(this.y, o2.y);
    }
    
    @Override
    public String toString() {
        return "(" + x + ", " + y + ")";
    }

    public Point(double x, double y) {
        this.x = x;
        this.y = y;
    }

    public Line line(Point other) {
        if (equals(other))
            return null;
        double a = other.y - y;
        double b = x - other.x;
        double c = -a * x - b * y;
        return new Line(a, b, c);
    }

    @Override
    public boolean equals(Object o) {
        if (this == o)
            return true;
        if (o == null || getClass() != o.getClass())
            return false;

        Point point = (Point) o;

        return Math.abs(x - point.x) <= GeometryUtils.epsilon && Math.abs(y - point.y) <= GeometryUtils.epsilon;
    }

    @Override
    public int hashCode() {
        int result;
        long temp;
        temp = x != +0.0d ? Double.doubleToLongBits(x) : 0L;
        result = (int) (temp ^ (temp >>> 32));
        temp = y != +0.0d ? Double.doubleToLongBits(y) : 0L;
        result = 31 * result + (int) (temp ^ (temp >>> 32));
        return result;
    }

    public double distance(Point other) {
        return GeometryUtils.fastHypot(x - other.x, y - other.y);
    }

    public double distance(Line line) {
        return Math.abs(line.a * x + line.b * y + line.c);
    }

    public double value() {
        return GeometryUtils.fastHypot(x, y);
    }

    public double angle() {
        return Math.atan2(y, x);
    }

    public static Point readPoint(InputReader in) {
        double x = in.readDouble();
        double y = in.readDouble();
        return new Point(x, y);
    }

    public Point rotate(double angle) {
        double nx = x * Math.cos(angle) - y * Math.sin(angle);
        double ny = y * Math.cos(angle) + x * Math.sin(angle);
        return new Point(nx, ny);
    }
}

class Angle {
    public final Point o;
    public final Point a;
    public final Point b;

    public Angle(Point o, Point a, Point b) {
        this.o = o;
        this.a = a;
        this.b = b;
    }

    public double value() {
        double ab = a.distance(b);
        double ao = a.distance(o);
        double bo = b.distance(o);
        return Math.acos((ao * ao + bo * bo - ab * ab) / (2 * ao * bo));
    }

}

class GeometryUtils {
    public static double epsilon = 1e-8;

    public static double fastHypot(double...x) {
        if (x.length == 0)
            return 0;
        else if (x.length == 1)
            return Math.abs(x[0]);
        else {
            double sumSquares = 0;
            for (double value : x)
                sumSquares += value * value;
            return Math.sqrt(sumSquares);
        }
    }

    public static double fastHypot(double x, double y) {
        return Math.sqrt(x * x + y * y);
    }

    public static double fastHypot(double[] x, double[] y) {
        if (x.length == 0)
            return 0;
        else if (x.length == 1)
            return Math.abs(x[0]- y[0]);
        else {
            double sumSquares = 0;
            for (int i = 0; i < x.length; i++) {
                double diff = x[i] - y[i];
                sumSquares += diff * diff;
            }
            return Math.sqrt(sumSquares);
        }
    }

    public static double fastHypot(int[] x, int[] y) {
        if (x.length == 0)
            return 0;
        else if (x.length == 1)
            return Math.abs(x[0]- y[0]);
        else {
            double sumSquares = 0;
            for (int i = 0; i < x.length; i++) {
                double diff = x[i] - y[i];
                sumSquares += diff * diff;
            }
            return Math.sqrt(sumSquares);
        }
    }

    public static double missileTrajectoryLength(double v, double angle, double g) {
        return (v * v * Math.sin(2 * angle)) / g;
    }

    public static double sphereVolume(double radius) {
        return 4 * Math.PI * radius * radius * radius / 3;
    }

    public static double triangleSquare(double first, double second, double third) {
        double p = (first + second + third) / 2;
        return Math.sqrt(p * (p - first) * (p - second) * (p - third));
    }

    public static double canonicalAngle(double angle) {
        while (angle > Math.PI)
            angle -= 2 * Math.PI;
        while (angle < -Math.PI)
            angle += 2 * Math.PI;
        return angle;
    }

    public static double positiveAngle(double angle) {
        while (angle > 2 * Math.PI - GeometryUtils.epsilon)
            angle -= 2 * Math.PI;
        while (angle < -GeometryUtils.epsilon)
            angle += 2 * Math.PI;
        return angle;
    }
}

class Line {
    public final double a;
    public final double b;
    public final double c;

    public Line(Point p, double angle) {
        a = Math.sin(angle);
        b = -Math.cos(angle);
        c = -p.x * a - p.y * b;
    }

    public Line(double a, double b, double c) {
        double h = GeometryUtils.fastHypot(a, b);
        this.a = a / h;
        this.b = b / h;
        this.c = c / h;
    }

    public Point intersect(Line other) {
        if (parallel(other))
            return null;
        double determinant = b * other.a - a * other.b;
        double x = (c * other.b - b * other.c) / determinant;
        double y = (a * other.c - c * other.a) / determinant;
        return new Point(x, y);
    }

    public boolean parallel(Line other) {
        return Math.abs(a * other.b - b * other.a) < GeometryUtils.epsilon;
    }

    public boolean contains(Point point) {
        return Math.abs(value(point)) < GeometryUtils.epsilon;
    }

    public Line perpendicular(Point point) {
        return new Line(-b, a, b * point.x - a * point.y);
    }

    public double value(Point point) {
        return a * point.x + b * point.y + c;
    }

    public Point[] intersect(Circle circle) {
        double distance = distance(circle.center);
        if (distance > circle.radius + GeometryUtils.epsilon)
            return new Point[0];
        Point intersection = intersect(perpendicular(circle.center));
        if (Math.abs(distance - circle.radius) < GeometryUtils.epsilon)
            return new Point[]{intersection};
        double shift = Math.sqrt(circle.radius * circle.radius - distance * distance);
        return new Point[]{new Point(intersection.x + shift * b, intersection.y - shift * a),
            new Point(intersection.x - shift * b, intersection.y + shift * a)};
    }

    public double distance(Point center) {
        return Math.abs(value(center));
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (o == null || getClass() != o.getClass()) return false;

        Line line = (Line) o;

        if (!parallel(line)) return false;
        if (Math.abs(a * line.c - c * line.a) > GeometryUtils.epsilon || Math.abs(b * line.c - c * line.b) > GeometryUtils.epsilon) return false;

        return true;
    }
}

class Circle {
    public final Point center;
    public final double radius;

    public Circle(Point center, double radius) {
        this.center = center;
        this.radius = radius;
    }

    public boolean contains(Point point) {
        return center.distance(point) < radius + GeometryUtils.epsilon;
    }

    public boolean strictContains(Point point) {
        return center.distance(point) < radius - GeometryUtils.epsilon;
    }

    public Point[] findTouchingPoints(Point point) {
        double distance = center.distance(point);
        if (distance < radius - GeometryUtils.epsilon)
            return new Point[0];
        if (distance < radius + GeometryUtils.epsilon)
            return new Point[]{point};
        Circle power = new Circle(point, Math.sqrt((distance - radius) * (distance + radius)));
        return intersect(power);
    }

    public Point[] intersect(Circle other) {
        double distance = center.distance(other.center);
        if (distance > radius + other.radius + GeometryUtils.epsilon || Math.abs(radius - other.radius) > distance + GeometryUtils.epsilon)
            return new Point[0];
        double p = (radius + other.radius + distance) / 2;
        double height = 2 * Math.sqrt(p * (p - radius) * (p - other.radius) * (p - distance)) / distance;
        double l1 = Math.sqrt(radius * radius - height * height);
        double l2 = Math.sqrt(other.radius * other.radius - height * height);
        if (radius * radius + distance * distance < other.radius * other.radius)
            l1 = -l1;
        if (radius * radius > distance * distance + other.radius * other.radius)
            l2 = -l2;
        Point middle = new Point((center.x * l2 + other.center.x * l1) / (l1 + l2),
            (center.y * l2 + other.center.y * l1) / (l1 + l2));
        Line line = center.line(other.center).perpendicular(middle);
        return line.intersect(this);
    }
}

class D implements Task {
    
    Point[] arr;
    int n, k, e;
    Point p;
    
    public void solve(int testNumber, InputReader in, OutputWriter out){
        n=in.readInt();
        k=in.readInt();
        e=in.readInt();
        int x0=in.readInt(), y0=in.readInt();
        p=new Point(x0, y0);
        arr=new Point[n];
        for (int i=0; i<n; i++) {
        	int x=in.readInt(), y=in.readInt();
        	arr[i]=new Point(x, y);
        }
        out.printLine(binarySearch());
    }
    
    double binarySearch() {
    	if (f1()) return 0.0;
    	double ini=GeometryUtils.epsilon, fim=3000.0, meio=0.5*(ini+fim);
    	for (int i=0; i<100; i++) {
    		if (f(meio)) fim=meio;
    		else ini=meio;
    		meio=0.5*(ini+fim);
    	}
    	return meio;
    }
    
    boolean f(double raio) {
    	double[][] pd=new double[n+1][n+1];
    	double ret=0.0;
    	Circle circulo=new Circle(p, raio);
    	for (int i=0; i<=n; i++) for (int j=0; j<=n; j++) {
    		if (i==0 && j==0) pd[i][j]=1.0;
    		else if (i==0) pd[i][j]=0.0;
    		else if (j==0) pd[i][j]=pd[i-1][j]*(1.0-f2(circulo, arr[i-1]));
    		else pd[i][j]=pd[i-1][j]*(1.0-f2(circulo, arr[i-1]))+pd[i-1][j-1]*f2(circulo, arr[i-1]);
    	}
    	for (int i=k; i<=n; i++) ret+=1.0*pd[n][i];
    	return ret>=0.001*(1000-e);
    }
    
    boolean f1() {
    	int ret=0;
    	for (int i=0; i<n; i++) if (p.equals(arr[i])) ret++;
    	return ret>=k;
    }
    
    double f2(Circle circulo, Point ponto) {
    	if (circulo.contains(ponto)) return 1.0;
    	return Math.exp(1.0-Math.pow(ponto.distance(circulo.center), 2.0)/Math.pow(circulo.radius, 2.0));
    }
        
}

class E implements Task {
    
	int[] arr=new int[10000010];
	
    public void solve(int testNumber, InputReader in, OutputWriter out){
    	int n=in.readInt(), m=in.readInt(), c=10000000, l2, r2, x=0;
    	long ret=0L, l, r;
    	for (int b=1; b<=n; b++) {
    		r=1L*b*b-1L;
    		l=Math.max(0L, 1L*b*b-m);
    		l2=(int)(Math.ceil(Math.sqrt(l)));
    		r2=(int)(Math.floor(Math.sqrt(r)));
    		ret+=2L*(r-l-r2+l2);
    		arr[-b-r2+c]++;
    		arr[-b-l2+1+c]--;
    		arr[-b+l2+c]++;
    		arr[-b+r2+1+c]--;
    	}
    	for (int i=0; i<=c; i++) {
    		x+=arr[i];
    		if (x>0) ret++;
    	}
    	out.printLine(ret);
    }
    
}

class InputReader {

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

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

    public int read() {
        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 int peek() {
        if (numChars == -1)
            return -1;
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                return -1;
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar];
    }

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

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

    public String readString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            if (Character.isValidCodePoint(c))
                res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    public boolean isSpaceChar(int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return isWhitespace(c);
    }

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

    private String readLine0() {
        StringBuilder buf = new StringBuilder();
        int c = read();
        while (c != '\n' && c != -1) {
            if (c != '\r')
                buf.appendCodePoint(c);
            c = read();
        }
        return buf.toString();
    }

    public String readLine() {
        String s = readLine0();
        while (s.trim().length() == 0)
            s = readLine0();
        return s;
    }

    public String readLine(boolean ignoreEmptyLines) {
        if (ignoreEmptyLines)
            return readLine();
        else
            return readLine0();
    }

    public BigInteger readBigInteger() {
        try {
            return new BigInteger(readString());
        } catch (NumberFormatException e) {
            throw new InputMismatchException();
        }
    }

    public char readCharacter() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        return (char) c;
    }

    public double readDouble() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        double res = 0;
        while (!isSpaceChar(c) && c != '.') {
            if (c == 'e' || c == 'E')
                return res * Math.pow(10, readInt());
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        if (c == '.') {
            c = read();
            double m = 1;
            while (!isSpaceChar(c)) {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, readInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                m /= 10;
                res += (c - '0') * m;
                c = read();
            }
        }
        return res * sgn;
    }

    public boolean isExhausted() {
        int value;
        while (isSpaceChar(value = peek()) && value != -1)
            read();
        return value == -1;
    }

    public String next() {
        return readString();
    }

    public SpaceCharFilter getFilter() {
        return filter;
    }

    public void setFilter(SpaceCharFilter filter) {
        this.filter = filter;
    }

    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}

class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void print(char[] array) {
        writer.print(array);
    }

    public void print(Object...objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(objects[i]);
        }
    }

    public void print(int[] array) {
        for (int i = 0; i < array.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(array[i]);
        }
    }

    public void print(long[] array) {
        for (int i = 0; i < array.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(array[i]);
        }
    }

    public void printLine(int[] array) {
        print(array);
        writer.println();
    }

    public void printLine(long[] array) {
        print(array);
        writer.println();
    }

    public void printLine() {
        writer.println();
    }

    public void printLine(Object...objects) {
        print(objects);
        writer.println();
    }

    public void print(char i) {
        writer.print(i);
    }

    public void printLine(char i) {
        writer.println(i);
    }

    public void printLine(char[] array) {
        writer.println(array);
    }

    public void printFormat(String format, Object...objects) {
        writer.printf(format, objects);
    }

    public void close() {
        writer.close();
    }

    public void flush() {
        writer.flush();
    }

    public void print(long i) {
        writer.print(i);
    }

    public void printLine(long i) {
        writer.println(i);
    }

    public void print(int i) {
        writer.print(i);
    }

    public void printLine(int i) {
        writer.println(i);
    }
}