定義 $f(x)$ 為滿足 $1 \leq y\leq x$ 且 $\gcd(x,y)=1$ 的整數 $y$ 的個數。這裡 $\gcd(x,y)$ 表示 $x$ 與 $y$ 的最大公因數。
定義 $g(x) = k \cdot f(x)$。
定義當 $t>1$ 時 $g^{(t)}(x)=g(g^{(t-1)}(x))$，且 $g^{(1)}(x)=g(x)$。
請求出 $g^{(t)}(n) \bmod 998\,244\,353$。
僅有一行包含三個整數 $n,k,t$（$1 \leq n,k,t \leq 998\,244\,352$）。
輸出一個整數，表示答案模 $998\,244\,353$ 的結果。
5 3 4
12
114514 1919 810
565299374
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