Walk on Graph

You are given a connected graph with N vertices and M edges. The vertices are numbered 1 to N. The i-th edge is an undirected edge of length C_i connecting Vertex A_i and Vertex B_i.

Additionally, an odd number MOD is given.

You will be given Q queries, which should be processed. The queries take the following form:

• Given in the i-th query are S_i, T_i and R_i. Print YES if there exists a path from Vertex S_i to Vertex T_i whose length is R_i modulo MOD, and print NO otherwise. A path may traverse the same edge multiple times, or go back using the edge it just used.

Here, in this problem, the length of a path is NOT the sum of the lengths of its edges themselves, but the length of the first edge used in the path gets multiplied by 1, the second edge gets multiplied by 2, the third edge gets multiplied by 4, and so on. (More formally, let L_1,...,L_k be the lengths of the edges used, in this order. The length of that path is the sum of L_i \times 2^{i-1}.)

Constraints

• 1 \leq N,M,Q \leq 50000
• 3 \leq MOD \leq 10^{6}
• MOD is odd.
• 1 \leq A_i,B_i\leq N
• 0 \leq C_i \leq MOD-1
• 1 \leq S_i,T_i \leq N
• 0 \leq R_i \leq MOD-1
• The given graph is connected. (It may contain self-loops or multiple edges.)

Input

Input is given from Standard Input in the following format:

N M Q MOD A_1 B_1 C_1 \vdots A_M B_M C_M S_1 T_1 R_1 \vdots S_Q T_Q R_Q

Output

Print the answers to the i-th query in the i-th line.

Examples

Input

3 2 2 2019 1 2 1 2 3 2 1 3 5 1 3 4

Output

YES NO

Input

6 6 3 2019 1 2 4 2 3 4 3 4 4 4 5 4 5 6 4 6 1 4 2 6 1110 3 1 1111 4 5 1112

Output

YES NO NO

Input

1 2 3 25 1 1 1 1 1 2 1 1 13 1 1 6 1 1 14

Output

YES YES YES

Input

10 15 10 15 1 2 1 2 3 6 3 4 6 2 5 1 5 6 1 4 7 6 1 8 11 2 9 6 5 10 11 9 10 11 3 6 1 2 5 1 2 7 11 9 10 11 5 6 11 1 3 5 9 8 3 7 7 7 7 10 13 4 1 10 9 3 12 10 10 14 9 2 1 6 6 5 8 8 4

Output

YES NO NO NO NO NO NO YES YES NO

inputFormat

Input

Input is given from Standard Input in the following format:

N M Q MOD A_1 B_1 C_1 \vdots A_M B_M C_M S_1 T_1 R_1 \vdots S_Q T_Q R_Q

outputFormat

Output

Print the answers to the i-th query in the i-th line.

Examples

Input

3 2 2 2019 1 2 1 2 3 2 1 3 5 1 3 4

Output

YES NO

Input

6 6 3 2019 1 2 4 2 3 4 3 4 4 4 5 4 5 6 4 6 1 4 2 6 1110 3 1 1111 4 5 1112

Output

YES NO NO

Input

1 2 3 25 1 1 1 1 1 2 1 1 13 1 1 6 1 1 14

Output

YES YES YES

Input

10 15 10 15 1 2 1 2 3 6 3 4 6 2 5 1 5 6 1 4 7 6 1 8 11 2 9 6 5 10 11 9 10 11 3 6 1 2 5 1 2 7 11 9 10 11 5 6 11 1 3 5 9 8 3 7 7 7 7 10 13 4 1 10 9 3 12 10 10 14 9 2 1 6 6 5 8 8 4

Output

YES NO NO NO NO NO NO YES YES NO

样例

3 2 2 2019
1 2 1
2 3 2
1 3 5
1 3 4

YES
NO

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