Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k, - k + 1, - k + 2, ..., - 2, - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.

Memory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)2t games in total. Since the answer can be very large, you should print it modulo 109 + 7. Please solve this problem for Memory.

Input

The first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.

Output

Print the number of possible games satisfying the conditions modulo 1 000 000 007 (109 + 7) in one line.

Examples

Input

1 2 2 1


Output

6


Input

1 1 1 2


Output

31


Input

2 12 3 1


Output

0

Note

In the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.
import java.io.IOException;
import java.util.Arrays;
import java.util.InputMismatchException;

public class MemoryAndScores {
	private static final int MOD = 1000000007;
	
    public static void main(String[] args) {
        FasterScanner sc = new FasterScanner();
        
        int A = sc.nextInt();
        int B = sc.nextInt();
        int K = sc.nextInt();
        int T = sc.nextInt();
        
        int Z = K * T;
        int L = Z + 1;

    	long[] curr = new long[L];
        long[] prev = new long[L];
    	long[] psum = new long[L + 1];
        prev[0] = 1;
        for (int t = 0; t < T; t++) {
        	prefixSum(prev, psum);
        	for (int i = 0; i < L; i++) {
//        		int lo = Math.max(i - K, 0);
//        		int hi = Math.min(i + K + 1, L);
//        		curr[i] = (psum[hi] - psum[lo] + MOD) % MOD;
        		
        		int lo = Math.max(i - K, -Z);
        		int hi = Math.min(i + K + 1, Z);
        		curr[i] = (rangeSum(psum, hi) - rangeSum(psum, lo) + MOD) % MOD;
        		if (curr[i] < 0) {
        			System.out.format("curr neg: i = %d, curr = %d\n", i, curr[i]);
        		}
        	}
        	System.arraycopy(curr, 0, prev, 0, L);
        }
        
//        System.out.println(Arrays.toString(prev));
        
        prefixSum(prev, psum);
        
        long ans = 0;
        for (int i = -L + 1; i < L; i++) {
        	int idx = i + A - B;
        	idx = Math.max(idx, -L);
        	idx = Math.min(idx, L);
//        	long fac;
//        	if (idx < 0) {
//        		int rev = Math.min(-idx + 1, L);
//        		fac = psum[L] - psum[rev]; 
//        	} else {
//        		fac = psum[idx] + psum[L] - prev[0];
//        	}
        	int pos = Math.abs(i);
//        	System.out.format("i = %d, fac = %d, amt = %d\n", i, fac, prev[pos]);
        	if (rangeSum(psum, idx) < 0) {
        		System.out.format("i = %d: wtf %d\n", i, rangeSum(psum, idx));
        		return;
        	}
        	ans += (rangeSum(psum, idx) * prev[pos]) % MOD;
        	ans %= MOD;
        	if (ans < 0) {
        		System.out.format("rip i = %d, ans = %d\n", i, ans);
        		return;
        	}
        }
        System.out.println(ans);
        
//        long ans = 0;
//        for (int i = Z + B - A + 1; i < L; i++) {
//        	ans += prev[i];
//        	ans %= MOD;
//        }
//        System.out.println(ans);
    }
    
    public static void prefixSum(long[] arr, long[] psum) {
    	psum[0] = 0;
    	for (int i = 1; i < psum.length; i++) {
    		psum[i] = (psum[i - 1] + arr[i - 1]) % MOD;
    	}
    }
    
    public static long rangeSum(long[] psum, int idx) {
    	int L = psum.length - 1;
    	if (idx < 0) {
    		int rev = Math.min(-idx + 1, L);
    		return (psum[L] - psum[rev] + MOD) % MOD; 
    	} else {
    		return (psum[idx] + psum[L] - psum[1] + MOD) % MOD;
    	}
    }

	public static class FasterScanner {
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = System.in.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

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

		public long nextLong() {
			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 int nextInt() {
			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 int[] nextIntArray(int n) {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

		public int[] nextIntArray(int n, int offset) {
			int[] arr = new int[n + offset];
			for (int i = 0; i < n; i++) {
				arr[i + offset] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n) {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}
			return arr;
		}

		public long[] nextLongArray(int n, int offset) {
			long[] arr = new long[n + offset];
			for (int i = 0; i < n; i++) {
				arr[i + offset] = nextLong();
			}
			return arr;
		}

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
	}
}