feat(scraper): add precision extraction, start_time, and submit support

Problem: problem pages contain floating-point precision requirements and
contest start timestamps that were not being extracted or stored. The
submit workflow also needed a foundation in the scraper layer.

Solution: add extract_precision() to base.py and propagate through all
scrapers into cache. Add start_time to ContestSummary and extract it
from AtCoder and Codeforces. Add SubmitResult model, abstract submit()
method, submit CLI case with get_language_id() resolution, stdin/env_extra
support in run_scraper, and a full AtCoder submit implementation; stub
the remaining platforms.

lua/cp/cache.lua

@@ -27,7 +27,7 @@
 ---@field multi_test? boolean
 ---@field memory_mb? number
 ---@field timeout_ms? number
----@field epsilon? number
+---@field precision? number
 ---@field combined_test? CombinedTest
 ---@field test_cases TestCase[]
 
@@ -231,7 +231,8 @@ function M.set_test_cases(
   timeout_ms,
   memory_mb,
   interactive,
-  multi_test
+  multi_test,
+  precision
 )
   vim.validate({
     platform = { platform, 'string' },
@@ -243,6 +244,7 @@ function M.set_test_cases(
     memory_mb = { memory_mb, { 'number', 'nil' }, true },
     interactive = { interactive, { 'boolean', 'nil' }, true },
     multi_test = { multi_test, { 'boolean', 'nil' }, true },
+    precision = { precision, { 'number', 'nil' }, true },
   })
 
   local index = cache_data[platform][contest_id].index_map[problem_id]
@@ -253,6 +255,7 @@ function M.set_test_cases(
   cache_data[platform][contest_id].problems[index].memory_mb = memory_mb
   cache_data[platform][contest_id].problems[index].interactive = interactive
   cache_data[platform][contest_id].problems[index].multi_test = multi_test
+  cache_data[platform][contest_id].problems[index].precision = precision
 
   M.save()
 end
@@ -278,7 +281,7 @@ end
 ---@param contest_id string
 ---@param problem_id? string
 ---@return number?
-function M.get_epsilon(platform, contest_id, problem_id)
+function M.get_precision(platform, contest_id, problem_id)
   vim.validate({
     platform = { platform, 'string' },
     contest_id = { contest_id, 'string' },
@@ -299,7 +302,7 @@ function M.get_epsilon(platform, contest_id, problem_id)
   end
 
   local problem_data = cache_data[platform][contest_id].problems[index]
-  return problem_data and problem_data.epsilon or nil
+  return problem_data and problem_data.precision or nil
 end
 
 ---@param file_path string
@@ -349,11 +352,24 @@ function M.set_contest_summaries(platform, contests)
     cache_data[platform][contest.id] = cache_data[platform][contest.id] or {}
     cache_data[platform][contest.id].display_name = contest.display_name
     cache_data[platform][contest.id].name = contest.name
+    if contest.start_time then
+      cache_data[platform][contest.id].start_time = contest.start_time
+    end
   end
 
   M.save()
 end
 
+---@param platform string
+---@param contest_id string
+---@return integer?
+function M.get_contest_start_time(platform, contest_id)
+  if not cache_data[platform] or not cache_data[platform][contest_id] then
+    return nil
+  end
+  return cache_data[platform][contest_id].start_time
+end
+
 function M.clear_all()
   cache_data = {}
   M.save()

lua/cp/scraper.lua

@@ -56,6 +56,12 @@ local function run_scraper(platform, subcommand, args, opts)
   env.PYTHONPATH = ''
   env.CONDA_PREFIX = ''
 
+  if opts and opts.env_extra then
+    for k, v in pairs(opts.env_extra) do
+      env[k] = v
+    end
+  end
+
   if opts and opts.ndjson then
     local uv = vim.uv
     local stdout = uv.new_pipe(false)
@@ -126,6 +132,9 @@ local function run_scraper(platform, subcommand, args, opts)
   end
 
   local sysopts = { text = true, timeout = 30000, env = env, cwd = plugin_path }
+  if opts and opts.stdin then
+    sysopts.stdin = opts.stdin
+  end
   if opts and opts.sync then
     local result = vim.system(cmd, sysopts):wait()
     return syshandle(result)
@@ -228,6 +237,7 @@ function M.scrape_all_tests(platform, contest_id, callback)
             memory_mb = ev.memory_mb or 0,
             interactive = ev.interactive or false,
             multi_test = ev.multi_test or false,
+            precision = ev.precision,
             problem_id = ev.problem_id,
           })
         end
@@ -236,4 +246,21 @@ function M.scrape_all_tests(platform, contest_id, callback)
   })
 end
 
+function M.submit(platform, contest_id, problem_id, language, source_code, credentials, callback)
+  local creds_json = vim.json.encode(credentials)
+  run_scraper(platform, 'submit', { contest_id, problem_id, language }, {
+    stdin = source_code,
+    env_extra = { CP_CREDENTIALS = creds_json },
+    on_exit = function(result)
+      if type(callback) == 'function' then
+        if result and result.success then
+          callback(result.data or { success = true })
+        else
+          callback({ success = false, error = result and result.error or 'unknown' })
+        end
+      end
+    end,
+  })
+end
+
 return M

lua/cp/setup.lua

@@ -130,7 +130,8 @@ local function start_tests(platform, contest_id, problems)
         ev.timeout_ms or 0,
         ev.memory_mb or 0,
         ev.interactive,
-        ev.multi_test
+        ev.multi_test,
+        ev.precision
       )
 
       local io_state = state.get_io_view_state()