In one one-dimensional world there are n platforms. Platform with index k (platforms are numbered from 1) is a segment with coordinates [(k - 1)m, (k - 1)m + l], and l < m. Grasshopper Bob starts to jump along the platforms from point 0, with each jump he moves exactly d units right. Find out the coordinate of the point, where Bob will fall down. The grasshopper falls down, if he finds himself not on the platform, but if he finds himself on the edge of the platform, he doesn't fall down.

Input

The first input line contains 4 integer numbers n, d, m, l (1 ≤ n, d, m, l ≤ 106, l < m) — respectively: amount of platforms, length of the grasshopper Bob's jump, and numbers m and l needed to find coordinates of the k-th platform: [(k - 1)m, (k - 1)m + l].

Output

Output the coordinates of the point, where the grosshopper will fall down. Don't forget that if Bob finds himself on the platform edge, he doesn't fall down.

Examples

Input

2 2 5 3


Output

4


Input

5 4 11 8


Output

20
import java.io.*;
import java.util.*;

public class B implements Runnable {
    public static void main(String[] args) {
        new B().run();
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        boolean eof;
        String buf;

        public FastScanner(String fileName) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(fileName));
            nextToken();
        }

        public FastScanner(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
            nextToken();
        }

        String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    eof = true;
                    break;
                }
            }
            String ret = buf;
            buf = eof ? "-1" : st.nextToken();
            return ret;
        }

        int nextInt() {
            return Integer.parseInt(nextToken());
        }

        long nextLong() {
            return Long.parseLong(nextToken());
        }

        double nextDouble() {
            return Double.parseDouble(nextToken());
        }

        void close() {
            try {
                br.close();
            } catch (Exception e) {

            }
        }

        boolean isEOF() {
            return eof;
        }
    }

    FastScanner sc;
    PrintWriter out;

    public void run() {
        Locale.setDefault(Locale.US);
        try {
            sc = new FastScanner(System.in);
            out = new PrintWriter(System.out);
            solve();
            sc.close();
            out.close();
        } catch (Throwable e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    int nextInt() {
        return sc.nextInt();
    }

    String nextToken() {
        return sc.nextToken();
    }

    long nextLong() {
        return sc.nextLong();
    }

    double nextDouble() {
        return sc.nextDouble();
    }

    void solve() {
        long n = nextInt();
        long d = nextInt();
        long m = nextInt();
        long l = nextInt();
        long[] e = new long[(int) m];
        Arrays.fill(e, -1);
        for (int i = 0, r = 0; i <= m; i++) {
            if (e[r] == -1) {
                e[r] = i * d;
            }
            r += d;
            r %= m;
        }
        long ans = ((n - 1) * m + l + d) / d * d;
        for (int i = (int) l + 1; i < m; i++) {
            if (e[i] != -1) {
                ans = Math.min(ans, e[i]);
            }
        }
        out.println(ans);
    }
}