{"raw_statement":[{"iden":"problem statement","content":"You are given a sequence of positive integers $A=(A_1,A_2,\\cdots,A_N)$ of length $N$.\nConsider dividing this sequence into $K$ non-empty contiguous subsequences. Among these $K$ contiguous subsequences, the number of ones whose sum of elements is at least $S$ will be called the **score**. Find the maximum value of the score."},{"iden":"constraints","content":"*   $1 \\leq K \\leq N \\leq 250000$\n*   $1 \\leq A_i \\leq 10^9$\n*   $1 \\leq S \\leq 10^{15}$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $K$ $S$\n$A_1$ $A_2$ $\\cdots$ $A_N$"},{"iden":"sample input 1","content":"4 3 6\n1 4 2 8"},{"iden":"sample output 1","content":"2\n\nIf the sequence is divided into $(1),(4,2),(8)$, the score will be $2$. No higher score can be achieved, so the answer is $2$."},{"iden":"sample input 2","content":"10 5 2\n1 1 1 1 1 1 1 1 1 1"},{"iden":"sample output 2","content":"5"},{"iden":"sample input 3","content":"10 5 3\n1 1 1 1 1 1 1 1 1 1"},{"iden":"sample output 3","content":"2"},{"iden":"sample input 4","content":"20 6 946667802\n786820955 250480341 710671229 946667801 19271059 404902145 251317818 22712439 520643153 344670307 274195604 561032101 140039457 543856068 521915711 857077284 499774361 419370025 744280520 249168130"},{"iden":"sample output 4","content":"6"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}