{"raw_statement":[{"iden":"problem statement","content":"In $2937$, DISCO creates a new universe called DISCOSMOS to celebrate its $1000$\\-th anniversary.\nDISCOSMOS can be described as an $H \\times W$ grid. Let $(i, j)$ $(1 \\leq i \\leq H, 1 \\leq j \\leq W)$ denote the square at the $i$\\-th row from the top and the $j$\\-th column from the left.\nAt time $0$, one robot will be placed onto each square. Each robot is one of the following three types:\n\n*   Type-H: Does not move at all.\n*   Type-R: If a robot of this type is in $(i, j)$ at time $t$, it will be in $(i, j+1)$ at time $t+1$. If it is in $(i, W)$ at time $t$, however, it will be instead in $(i, 1)$ at time $t+1$. (The robots do not collide with each other.)\n*   Type-D: If a robot of this type is in $(i, j)$ at time $t$, it will be in $(i+1, j)$ at time $t+1$. If it is in $(H, j)$ at time $t$, however, it will be instead in $(1, j)$ at time $t+1$.\n\nThere are $3^{H \\times W}$ possible ways to place these robots. In how many of them will every square be occupied by one robot at times $0, T, 2T, 3T, 4T$, and all subsequent multiples of $T$?\nSince the count can be enormous, compute it modulo $(10^9 + 7)$."},{"iden":"constraints","content":"*   $1 \\leq H \\leq 10^9$\n*   $1 \\leq W \\leq 10^9$\n*   $1 \\leq T \\leq 10^9$\n*   $H, W, T$ are all integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$H$ $W$ $T$"},{"iden":"sample input 1","content":"2 2 1"},{"iden":"sample output 1","content":"9\n\nShown below are some of the ways to place the robots that satisfy the condition, where `.`, `>`, and `v` stand for Type-H, Type-R, and Type-D, respectively:\n\n\\>>  ..  vv\n..  ..  vv"},{"iden":"sample input 2","content":"869 120 1001"},{"iden":"sample output 2","content":"672919729"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}