Given a sequence $a_1, a_2, \ldots, a_n$ of length $n$, where each number is between $0$ and $v - 1$, there are $m$ operations.

Operation 1: For a given range, determine if it is possible to choose two non-empty disjoint sets of indices $X$ and $Y$ such that:

1. $X \cap Y = \emptyset$.
2. Let the contribution of an element $i$ in set $X$ be $a_i + 1$. The sum of contributions of elements in set $X$ must equal the sum of contributions of elements in set $Y$. If such sets can be chosen, output Yuno, otherwise output Yuki.

Operation 2: Modify the numbers in a range $[l, r]$ such that for all $l \leq i \leq r$, $a_i = a_i^3 \bmod v$.

Input

The first line contains three integers $n, m, v$, as described above.

The next line contains $n$ integers, representing the sequence $a$.

The next $m$ lines each contain three integers $opt, l, r$, representing the operation type ($1$ or $2$) and the range $[l, r]$.

Output

For each query, output a single line containing the string Yuno or Yuki indicating whether the two sets can be chosen.

Examples

Input 1

20 20 152
3 26 133 54 79 81 72 109 66 91 82 100 35 23 104 17 51 114 12 58
2 1 17
2 6 12
1 1 12
2 3 5
2 11 11
2 7 19
2 6 15
1 5 12
1 1 9
1 10 19
2 3 19
2 6 20
2 1 13
2 1 15
2 1 9
1 1 1
2 1 7
2 7 19
2 6 19
2 3 6

Output 1

Yuno
Yuno
Yuno
Yuno
Yuki

Note

Idea: nzhtl1477, Solution: nzhtl1477, Code: nzhtl1477, Data: nzhtl1477

For $100\%$ of the data, $1 \leq n, m \leq 10^5$, $1 \leq v \leq 1000$. The data is not graded.