import sys def main(): input = sys.stdin.read().split() ptr = 0 N = int(input[ptr]) ptr += 1 Q = int(input[ptr]) ptr += 1 P = int(input[ptr]) ptr += 1 A = list(map(lambda x: int(x) % P, input[ptr:ptr+N])) ptr += N # Precompute the possible remainders for each interval [i, j] pre = [[0] * (N + 1) for _ in range(N + 1)] # pre[i][j] is the bitmask for interval [i, j] for i in range(N): current_mask = 0 a = A[i] current_mask |= 1 << a pre[i+1][i+1] = current_mask for j in range(i + 1, N): a_j = A[j] temp_mask = 0 mask = pre[i+1][j] # previous mask up to j (exclusive) # Multiply each existing remainder by a_j and add a_j itself while mask: lsb = mask & -mask r = (lsb.bit_length() - 1) product = (r * a_j) % P temp_mask |= 1 << product mask ^= lsb # Add the current a_j itself (as a new subset) temp_mask |= 1 << a_j # Combine with previous subsets (which do not include a_j) new_mask = pre[i+1][j] | temp_mask pre[i+1][j+1] = new_mask # Precompute the prefix sum of zeros to quickly check for K=0 zero_prefix = [0] * (N + 1) for i in range(N): zero_prefix[i+1] = zero_prefix[i] + (A[i] == 0) # Process each query output = [] for _ in range(Q): L = int(input[ptr]) ptr += 1 R = int(input[ptr]) ptr += 1 K = int(input[ptr]) ptr += 1 if K == 0: # Check if there's at least one zero in the interval zeros = zero_prefix[R] - zero_prefix[L-1] output.append("Yes" if zeros > 0 else "No") else: # Check if there are non-zero elements total = R - L + 1 zeros = zero_prefix[R] - zero_prefix[L-1] if zeros == total: output.append("No") continue # Check the precomputed mask mask = pre[L][R] if (mask >> K) & 1: output.append("Yes") else: output.append("No") print('\n'.join(output)) if __name__ == "__main__": main()