MOD = 10**9 + 7 def main(): import sys input = sys.stdin.read().split() idx = 0 N = int(input[idx]); idx +=1 M_P = int(input[idx]); idx +=1 M_q = int(input[idx]); idx +=1 L = int(input[idx]); idx +=1 S = list(map(int, input[idx:idx+N])) idx += N # Precompute factorial and inverse factorial for combinations max_n = M_P + N - 1 fact = [1] * (max_n + 1) for i in range(1, max_n + 1): fact[i] = fact[i-1] * i % MOD inv_fact = [1] * (max_n + 1) inv_fact[max_n] = pow(fact[max_n], MOD-2, MOD) for i in range(max_n-1, -1, -1): inv_fact[i] = inv_fact[i+1] * (i+1) % MOD def comb(n, k): if n < 0 or k < 0 or n < k: return 0 return fact[n] * inv_fact[k] % MOD * inv_fact[n -k] % MOD # Initialize DP dp_current = [ [0]*(M_q +1) for _ in range(N+1) ] dp_current[0][0] = 1 for i in range(N): s_i = S[i] dp_next = [ [0]*(M_q +1) for _ in range(N+1) ] diff = [ [0]*(M_q +2) for _ in range(N+2) ] # diff[k][sum_q] for k_prev in range(N+1): for sum_q_prev in range(M_q +1): val = dp_current[k_prev][sum_q_prev] if val == 0: continue # Case 1: q_i = 0 dp_next[k_prev][sum_q_prev] = (dp_next[k_prev][sum_q_prev] + val) % MOD # Case 2: q_i >=1 k_next = k_prev + 1 if k_next > N: continue # Compute start and end for sum_q_next lower = L * k_next - M_P start = max(sum_q_prev + 1, lower) end = min(sum_q_prev + s_i, M_q) if start > end: continue # Update diff array diff[k_next][start] = (diff[k_next][start] + val) % MOD if end +1 <= M_q: diff[k_next][end +1] = (diff[k_next][end +1] - val) % MOD # Apply diff to dp_next for k_next in range(N+1): current = 0 for sum_q in range(M_q +1): current = (current + diff[k_next][sum_q]) % MOD dp_next[k_next][sum_q] = (dp_next[k_next][sum_q] + current) % MOD dp_current = dp_next # Calculate the answer ans = 0 for k in range(N+1): for sum_q in range(M_q +1): if sum_q > M_q: continue sum_a = L * k - sum_q if sum_a < 0 or sum_a > M_P: continue rem = M_P - sum_a c = comb(rem + N -1, N-1) ans = (ans + dp_current[k][sum_q] * c) % MOD print(ans % MOD) if __name__ == '__main__': main()