{"problem":{"name":"guruguru","description":{"content":"Snuke is buying a lamp. The light of the lamp can be adjusted to $m$ levels of brightness, represented by integers from $1$ through $m$, by the two buttons on the remote control. The first button is a","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc077_c"},"statements":[{"statement_type":"Markdown","content":"Snuke is buying a lamp. The light of the lamp can be adjusted to $m$ levels of brightness, represented by integers from $1$ through $m$, by the two buttons on the remote control.\nThe first button is a \"forward\" button. When this button is pressed, the brightness level is increased by $1$, except when the brightness level is $m$, in which case the brightness level becomes $1$.\nThe second button is a \"favorite\" button. When this button is pressed, the brightness level becomes the favorite brightness level $x$, which is set when the lamp is purchased.\nSnuke is thinking of setting the favorite brightness level $x$ so that he can efficiently adjust the brightness. He is planning to change the brightness $n-1$ times. In the $i$\\-th change, the brightness level is changed from $a_i$ to $a_{i+1}$. The initial brightness level is $a_1$. Find the number of times Snuke needs to press the buttons when $x$ is set to minimize this number.\n\n## Constraints\n\n*   $2 \\leq n,m \\leq 10^5$\n*   $1 \\leq a_i\\leq m$\n*   $a_i \\neq a_{i+1}$\n*   $n$, $m$ and $a_i$ are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$n$ $m$\n$a_1$ $a_2$ … $a_n$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc077_c","tags":[],"sample_group":[["4 6\n1 5 1 4","5\n\nWhen the favorite brightness level is set to $1$, $2$, $3$, $4$, $5$ and $6$, Snuke needs to press the buttons $8$, $9$, $7$, $5$, $6$ and $9$ times, respectively. Thus, Snuke should set the favorite brightness level to $4$. In this case, the brightness is adjusted as follows:\n\n*   In the first change, press the favorite button once, then press the forward button once.\n*   In the second change, press the forward button twice.\n*   In the third change, press the favorite button once."],["10 10\n10 9 8 7 6 5 4 3 2 1","45"]],"created_at":"2026-03-03 11:01:14"}}