Alice has got addicted to a game called Sirtet recently.

In Sirtet, player is given an n × m grid. Initially a_{i,j} cubes are stacked up in the cell (i,j). Two cells are called adjacent if they share a side. Player can perform the following operations: 

  * stack up one cube in two adjacent cells; 
  * stack up two cubes in one cell. 



Cubes mentioned above are identical in height.

Here is an illustration of the game. States on the right are obtained by performing one of the above operations on the state on the left, and grey cubes are added due to the operation.

<image>

Player's goal is to make the height of all cells the same (i.e. so that each cell has the same number of cubes in it) using above operations. 

Alice, however, has found out that on some starting grids she may never reach the goal no matter what strategy she uses. Thus, she is wondering the number of initial grids such that 

  * L ≤ a_{i,j} ≤ R for all 1 ≤ i ≤ n, 1 ≤ j ≤ m; 
  * player can reach the goal using above operations. 



Please help Alice with it. Notice that the answer might be large, please output the desired value modulo 998,244,353.

Input

The only line contains four integers n, m, L and R (1≤ n,m,L,R ≤ 10^9, L ≤ R, n ⋅ m ≥ 2).

Output

Output one integer, representing the desired answer modulo 998,244,353.

Examples

Input


2 2 1 1


Output


1


Input


1 2 1 2


Output


2

Note

In the first sample, the only initial grid that satisfies the requirements is a_{1,1}=a_{2,1}=a_{1,2}=a_{2,2}=1. Thus the answer should be 1.

In the second sample, initial grids that satisfy the requirements are a_{1,1}=a_{1,2}=1 and a_{1,1}=a_{1,2}=2. Thus the answer should be 2.
import java.io.*;
import java.util.*;

import static java.lang.Math.*;
import static java.util.Arrays.*;

public class cf1332e {

    static Map<Long, Integer> f = new HashMap<>(), g = new HashMap<>();

    public static void main(String[] args) throws IOException {
        int n = rni(), m = ni(), l = ni(), r = ni();
        long nm = (long) n * m;
        int N = r - l + 1, E = l % 2 == 0 ? (N + 1) / 2 : N / 2;
        f.put(0L, 1);
        f.put(1L, E % mmod);
        g.put(0L, 0);
        g.put(1L, (N - E) % mmod);
        prln(nm % 2 == 1 ? mpow(N, nm) : f(nm));
        close();
    }

    static int f(long n) {
        if (f.containsKey(n)) {
            return f.get(n);
        }
        f.put(n, madd(mmul(f(n / 2), f((n + 1) / 2)), mmul(g(n / 2), g((n + 1) / 2))));
        return f.get(n);
    }

    static int g(long n) {
        if (g.containsKey(n)) {
            return g.get(n);
        }
        g.put(n, madd(mmul(f(n / 2), g((n + 1) / 2)), mmul(g(n / 2), f((n + 1) / 2))));
        return g.get(n);
    }

    static int mmod = 998244353;

    static int madd(int a, int b) {
        return (a + b) % mmod;
    }

    static int madd(int... a) {
        int ans = a[0];
        for (int i = 1; i < a.length; ++i) {
            ans = madd(ans, a[i]);
        }
        return ans;
    }

    static int msub(int a, int b) {
        return (a - b + mmod) % mmod;
    }

    static int mmul(int a, int b) {
        return (int) ((long) a * b % mmod);
    }

    static int mmul(int... a) {
        int ans = a[0];
        for (int i = 1; i < a.length; ++i) {
            ans = mmul(ans, a[i]);
        }
        return ans;
    }

    static int minv(int x) {
        return mpow(x, mmod - 2);
    }

    static int mpow(int a, long b) {
        if (a == 0) {
            return 0;
        }
        int ans = 1;
        while (b > 0) {
            if ((b & 1) > 0) {
                ans = mmul(ans, a);
            }
            a = mmul(a, a);
            b >>= 1;
        }
        return ans;
    }

    static int mpow(int a, int b) {
        if (a == 0) {
            return 0;
        }
        int ans = 1;
        while (b > 0) {
            if ((b & 1) > 0) {
                ans = mmul(ans, a);
            }
            a = mmul(a, a);
            b >>= 1;
        }
        return ans;
    }

    static BufferedReader __in = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter __out = new PrintWriter(new OutputStreamWriter(System.out));
    static StringTokenizer input;
    static Random __rand = new Random();

    // references
    // IBIG = 1e9 + 7
    // IMAX ~= 2e9
    // LMAX ~= 9e18

    // constants
    static final int IBIG = 1000000007;
    static final int IMAX = 2147483647;
    static final int IMIN = -2147483648;
    static final long LMAX = 9223372036854775807L;
    static final long LMIN = -9223372036854775808L;
    // math util
    static int minof(int a, int b, int c) {return min(a, min(b, c));}
    static int minof(int... x) {if (x.length == 1) return x[0]; if (x.length == 2) return min(x[0], x[1]); if (x.length == 3) return min(x[0], min(x[1], x[2])); int min = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i]; return min;}
    static long minof(long a, long b, long c) {return min(a, min(b, c));}
    static long minof(long... x) {if (x.length == 1) return x[0]; if (x.length == 2) return min(x[0], x[1]); if (x.length == 3) return min(x[0], min(x[1], x[2])); long min = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i]; return min;}
    static int maxof(int a, int b, int c) {return max(a, max(b, c));}
    static int maxof(int... x) {if (x.length == 1) return x[0]; if (x.length == 2) return max(x[0], x[1]); if (x.length == 3) return max(x[0], max(x[1], x[2])); int max = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i]; return max;}
    static long maxof(long a, long b, long c) {return max(a, max(b, c));}
    static long maxof(long... x) {if (x.length == 1) return x[0]; if (x.length == 2) return max(x[0], x[1]); if (x.length == 3) return max(x[0], max(x[1], x[2])); long max = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i]; return max;}
    static int powi(int a, int b) {if (a == 0) return 0; int ans = 1; while (b > 0) {if ((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
    static long powl(long a, int b) {if (a == 0) return 0; long ans = 1; while (b > 0) {if ((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
    static int fli(double d) {return (int) d;}
    static int cei(double d) {return (int) ceil(d);}
    static long fll(double d) {return (long) d;}
    static long cel(double d) {return (long) ceil(d);}
    static int gcf(int a, int b) {return b == 0 ? a : gcf(b, a % b);}
    static long gcf(long a, long b) {return b == 0 ? a : gcf(b, a % b);}
    static int lcm(int a, int b) {return a * b / gcf(a, b);}
    static long lcm(long a, long b) {return a * b / gcf(a, b);}
    static int randInt(int min, int max) {return __rand.nextInt(max - min + 1) + min;}
    static long mix(long x) {x += 0x9e3779b97f4a7c15L; x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9L; x = (x ^ (x >> 27)) * 0x94d049bb133111ebL; return x ^ (x >> 31);}
    // array util
    static void reverse(int[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {int swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(long[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {long swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(double[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {double swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(char[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {char swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void shuffle(int[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); int swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void shuffle(long[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); long swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void shuffle(double[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); double swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void rsort(int[] a) {shuffle(a); sort(a);}
    static void rsort(long[] a) {shuffle(a); sort(a);}
    static void rsort(double[] a) {shuffle(a); sort(a);}
    static int[] copy(int[] a) {int[] ans = new int[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static long[] copy(long[] a) {long[] ans = new long[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static double[] copy(double[] a) {double[] ans = new double[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static char[] copy(char[] a) {char[] ans = new char[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    // graph util
    static List<List<Integer>> g(int n) {List<List<Integer>> g = new ArrayList<>(); for (int i = 0; i < n; ++i) g.add(new ArrayList<>()); return g;}
    static List<Set<Integer>> sg(int n) {List<Set<Integer>> g = new ArrayList<>(); for (int i = 0; i < n; ++i) g.add(new HashSet<>()); return g;}
    static void c(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).add(v); g.get(v).add(u);}
    static void cto(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).add(v);}
    static void dc(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).remove(v); g.get(v).remove(u);}
    static void dcto(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).remove(v);}
    // input
    static void r() throws IOException {input = new StringTokenizer(rline());}
    static int ri() throws IOException {return Integer.parseInt(rline());}
    static long rl() throws IOException {return Long.parseLong(rline());}
    static double rd() throws IOException {return Double.parseDouble(rline());}
    static int[] ria(int n) throws IOException {int[] a = new int[n]; r(); for (int i = 0; i < n; ++i) a[i] = ni(); return a;}
    static int[] riam1(int n) throws IOException {int[] a = new int[n]; r(); for (int i = 0; i < n; ++i) a[i] = ni() - 1; return a;}
    static long[] rla(int n) throws IOException {long[] a = new long[n]; r(); for (int i = 0; i < n; ++i) a[i] = nl(); return a;}
    static double[] rda(int n) throws IOException {double[] a = new double[n]; r(); for (int i = 0; i < n; ++i) a[i] = nd(); return a;}
    static char[] rcha() throws IOException {return rline().toCharArray();}
    static String rline() throws IOException {return __in.readLine();}
    static String n() {return input.nextToken();}
    static int rni() throws IOException {r(); return ni();}
    static int ni() {return Integer.parseInt(n());}
    static long rnl() throws IOException {r(); return nl();}
    static long nl() {return Long.parseLong(n());}
    static double rnd() throws IOException {r(); return nd();}
    static double nd() {return Double.parseDouble(n());}
    static List<List<Integer>> rg(int n, int m) throws IOException {List<List<Integer>> g = g(n); for (int i = 0; i < m; ++i) c(g, rni() - 1, ni() - 1); return g;}
    static void rg(List<List<Integer>> g, int m) throws IOException {for (int i = 0; i < m; ++i) c(g, rni() - 1, ni() - 1);}
    static List<List<Integer>> rdg(int n, int m) throws IOException {List<List<Integer>> g = g(n); for (int i = 0; i < m; ++i) cto(g, rni() - 1, ni() - 1); return g;}
    static void rdg(List<List<Integer>> g, int m) throws IOException {for (int i = 0; i < m; ++i) cto(g, rni() - 1, ni() - 1);}
    static List<Set<Integer>> rsg(int n, int m) throws IOException {List<Set<Integer>> g = sg(n); for (int i = 0; i < m; ++i) c(g, rni() - 1, ni() - 1); return g;}
    static void rsg(List<Set<Integer>> g, int m) throws IOException {for (int i = 0; i < m; ++i) c(g, rni() - 1, ni() - 1);}
    static List<Set<Integer>> rdsg(int n, int m) throws IOException {List<Set<Integer>> g = sg(n); for (int i = 0; i < m; ++i) cto(g, rni() - 1, ni() - 1); return g;}
    static void rdsg(List<Set<Integer>> g, int m) throws IOException {for (int i = 0; i < m; ++i) cto(g, rni() - 1, ni() - 1);}
    // output
    static void pr(int i) {__out.print(i);}
    static void prln(int i) {__out.println(i);}
    static void pr(long l) {__out.print(l);}
    static void prln(long l) {__out.println(l);}
    static void pr(double d) {__out.print(d);}
    static void prln(double d) {__out.println(d);}
    static void pr(char c) {__out.print(c);}
    static void prln(char c) {__out.println(c);}
    static void pr(char[] s) {__out.print(new String(s));}
    static void prln(char[] s) {__out.println(new String(s));}
    static void pr(String s) {__out.print(s);}
    static void prln(String s) {__out.println(s);}
    static void pr(Object o) {__out.print(o);}
    static void prln(Object o) {__out.println(o);}
    static void prln() {__out.println();}
    static void pryes() {prln("yes");}
    static void pry() {prln("Yes");}
    static void prY() {prln("YES");}
    static void prno() {prln("no");}
    static void prn() {prln("No");}
    static void prN() {prln("NO");}
    static void pryesno(boolean b) {prln(b ? "yes" : "no");};
    static void pryn(boolean b) {prln(b ? "Yes" : "No");}
    static void prYN(boolean b) {prln(b ? "YES" : "NO");}
    static void prln(int... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
    static void prln(long... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
    static void prln(double... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
    static <T> void prln(Collection<T> c) {int n = c.size() - 1; Iterator<T> iter = c.iterator(); for (int i = 0; i < n; pr(iter.next()), pr(' '), ++i); if (n >= 0) prln(iter.next()); else prln();}
    static void h() {prln("hlfd"); flush();}
    static void flush() {__out.flush();}
    static void close() {__out.close();}}