cannot insert into column "id"

export const productsTable = pgTable("products", {
  id: integer().primaryKey().generatedAlwaysAsIdentity({ startWith: 1000 }),
  name: varchar({ length: 255 }).notNull(),
})

const result = await db
  .insert(productsTable)
  .values([
    { name: 'test' },
    { name: 'test2' },
  ])

error: cannot insert into column "id"
    at .../node_modules/.pnpm/pg-pool@3.8.0_pg@8.14.0/node_modules/pg-pool/index.js:45:11
    at processTicksAndRejections (node:internal/process/task_queues:105:5)