human
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.


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.
# Ent
Here strategy she uses?
assistant
#Here strategy she uses.
er your code here. Read input from STDIN. Print output to STDOUT# ===============================================================================================
# importing some useful libraries.
from __future__ import division, print_function
from fractions import Fraction
import sys
import os
from io import BytesIO, IOBase
from itertools import *
import bisect
from heapq import *
from math import ceil, floor
from copy import *
from collections import deque, defaultdict
from collections import Counter as counter  # Counter(list)  return a dict with {key: count}
from itertools import combinations  # if a = [1,2,3] then print(list(comb(a,2))) -----> [(1, 2), (1, 3), (2, 3)]
from itertools import permutations as permutate
from bisect import bisect_left as bl
from operator import *
# If the element is already present in the list,

# the left most position where element has to be inserted is returned.
from bisect import bisect_right as br
from bisect import bisect

# If the element is already present in the list,
# the right most position where element has to be inserted is returned

# ==============================================================================================
# fast I/O region

BUFSIZE = 8192
from sys import stderr

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not...