#384852 (Go) No.895 MESE

• 問題: No.895 MESE
• ユーザー: maguroguma
• 提出日時: 2019-09-28 01:30:21
• 言語: Go (1.22.1)
• 結果: AC
• 実行時間: 132 ms / 2,000 ms
• コード長: 10,115 bytes
• コンパイル時間: 16,272 ms
• コンパイル使用メモリ: 223,184 KB
• 実行使用メモリ: 15,864 KB
• 最終ジャッジ日時: 2024-09-25 04:49:57
• 合計ジャッジ時間: 20,080 ms
• ジャッジサーバーID （参考情報）: judge2 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	128 ms; 15,864 KB
testcase_01	AC	128 ms; 15,864 KB
testcase_02	AC	130 ms; 15,864 KB
testcase_03	AC	130 ms; 15,864 KB
testcase_04	AC	130 ms; 15,860 KB
testcase_05	AC	129 ms; 15,860 KB
testcase_06	AC	130 ms; 15,860 KB
testcase_07	AC	130 ms; 15,860 KB
testcase_08	AC	132 ms; 15,864 KB
testcase_09	AC	131 ms; 15,860 KB
testcase_10	AC	130 ms; 15,864 KB
testcase_11	AC	130 ms; 15,860 KB
testcase_12	AC	129 ms; 15,864 KB
testcase_13	AC	130 ms; 15,860 KB
testcase_14	AC	132 ms; 15,864 KB
testcase_15	AC	132 ms; 15,860 KB
testcase_16	AC	130 ms; 15,860 KB
testcase_17	AC	129 ms; 15,860 KB
testcase_18	AC	132 ms; 15,860 KB
testcase_19	AC	132 ms; 15,860 KB
testcase_20	AC	132 ms; 15,864 KB
testcase_21	AC	130 ms; 15,860 KB
testcase_22	AC	128 ms; 15,860 KB
testcase_23	AC	129 ms; 15,860 KB
testcase_24	AC	130 ms; 15,864 KB
testcase_25	AC	131 ms; 15,860 KB
testcase_26	AC	130 ms; 15,860 KB
testcase_27	AC	130 ms; 15,860 KB
testcase_28	AC	131 ms; 15,860 KB

ソースコード

package main

import (
	"bufio"
	"errors"
	"fmt"
	"io"
	"math"
	"os"
	"strconv"
)

/*********** I/O ***********/

var (
	// ReadString returns a WORD string.
	ReadString func() string
	stdout     *bufio.Writer
)

func init() {
	ReadString = newReadString(os.Stdin)
	stdout = bufio.NewWriter(os.Stdout)
}

func newReadString(ior io.Reader) func() string {
	r := bufio.NewScanner(ior)
	// r.Buffer(make([]byte, 1024), int(1e+11)) // for AtCoder
	r.Buffer(make([]byte, 1024), int(1e+9)) // for Codeforces
	// Split sets the split function for the Scanner. The default split function is ScanLines.
	// Split panics if it is called after scanning has started.
	r.Split(bufio.ScanWords)

	return func() string {
		if !r.Scan() {
			panic("Scan failed")
		}
		return r.Text()
	}
}

// ReadInt returns an integer.
func ReadInt() int {
	return int(readInt64())
}
func ReadInt2() (int, int) {
	return int(readInt64()), int(readInt64())
}
func ReadInt3() (int, int, int) {
	return int(readInt64()), int(readInt64()), int(readInt64())
}
func ReadInt4() (int, int, int, int) {
	return int(readInt64()), int(readInt64()), int(readInt64()), int(readInt64())
}

// ReadInt64 returns as integer as int64.
func ReadInt64() int64 {
	return readInt64()
}
func ReadInt64_2() (int64, int64) {
	return readInt64(), readInt64()
}
func ReadInt64_3() (int64, int64, int64) {
	return readInt64(), readInt64(), readInt64()
}
func ReadInt64_4() (int64, int64, int64, int64) {
	return readInt64(), readInt64(), readInt64(), readInt64()
}

func readInt64() int64 {
	i, err := strconv.ParseInt(ReadString(), 0, 64)
	if err != nil {
		panic(err.Error())
	}
	return i
}

// ReadIntSlice returns an integer slice that has n integers.
func ReadIntSlice(n int) []int {
	b := make([]int, n)
	for i := 0; i < n; i++ {
		b[i] = ReadInt()
	}
	return b
}

// ReadInt64Slice returns as int64 slice that has n integers.
func ReadInt64Slice(n int) []int64 {
	b := make([]int64, n)
	for i := 0; i < n; i++ {
		b[i] = ReadInt64()
	}
	return b
}

// ReadFloat64 returns an float64.
func ReadFloat64() float64 {
	return float64(readFloat64())
}

func readFloat64() float64 {
	f, err := strconv.ParseFloat(ReadString(), 64)
	if err != nil {
		panic(err.Error())
	}
	return f
}

// ReadFloatSlice returns an float64 slice that has n float64.
func ReadFloat64Slice(n int) []float64 {
	b := make([]float64, n)
	for i := 0; i < n; i++ {
		b[i] = ReadFloat64()
	}
	return b
}

// ReadRuneSlice returns a rune slice.
func ReadRuneSlice() []rune {
	return []rune(ReadString())
}

/*********** Debugging ***********/

// ZeroPaddingRuneSlice returns binary expressions of integer n with zero padding.
// For debugging use.
func ZeroPaddingRuneSlice(n, digitsNum int) []rune {
	sn := fmt.Sprintf("%b", n)

	residualLength := digitsNum - len(sn)
	if residualLength <= 0 {
		return []rune(sn)
	}

	zeros := make([]rune, residualLength)
	for i := 0; i < len(zeros); i++ {
		zeros[i] = '0'
	}

	res := []rune{}
	res = append(res, zeros...)
	res = append(res, []rune(sn)...)

	return res
}

/*********** DP sub-functions ***********/

// ChMin accepts a pointer of integer and a target value.
// If target value is SMALLER than the first argument,
//	then the first argument will be updated by the second argument.
func ChMin(updatedValue *int, target int) bool {
	if *updatedValue > target {
		*updatedValue = target
		return true
	}
	return false
}

// ChMax accepts a pointer of integer and a target value.
// If target value is LARGER than the first argument,
//	then the first argument will be updated by the second argument.
func ChMax(updatedValue *int, target int) bool {
	if *updatedValue < target {
		*updatedValue = target
		return true
	}
	return false
}

// NthBit returns nth bit value of an argument.
// n starts from 0.
func NthBit(num, nth int) int {
	return num >> uint(nth) & 1
}

// OnBit returns the integer that has nth ON bit.
// If an argument has nth ON bit, OnBit returns the argument.
func OnBit(num, nth int) int {
	return num | (1 << uint(nth))
}

// OffBit returns the integer that has nth OFF bit.
// If an argument has nth OFF bit, OffBit returns the argument.
func OffBit(num, nth int) int {
	return num & ^(1 << uint(nth))
}

// PopCount returns the number of ON bit of an argument.
func PopCount(num int) int {
	res := 0

	for i := 0; i < 70; i++ {
		if ((num >> uint(i)) & 1) == 1 {
			res++
		}
	}

	return res
}

/*********** Arithmetic ***********/

// Max returns the max integer among input set.
// This function needs at least 1 argument (no argument causes panic).
func Max(integers ...int) int {
	m := integers[0]
	for i, integer := range integers {
		if i == 0 {
			continue
		}
		if m < integer {
			m = integer
		}
	}
	return m
}

// Min returns the min integer among input set.
// This function needs at least 1 argument (no argument causes panic).
func Min(integers ...int) int {
	m := integers[0]
	for i, integer := range integers {
		if i == 0 {
			continue
		}
		if m > integer {
			m = integer
		}
	}
	return m
}

// DigitSum returns digit sum of a decimal number.
// DigitSum only accept a positive integer.
func DigitSum(n int) int {
	if n < 0 {
		return -1
	}

	res := 0

	for n > 0 {
		res += n % 10
		n /= 10
	}

	return res
}

// DigitNumOfDecimal returns digits number of n.
// n is non negative number.
func DigitNumOfDecimal(n int) int {
	res := 0

	for n > 0 {
		n /= 10
		res++
	}

	return res
}

// Sum returns multiple integers sum.
func Sum(integers ...int) int {
	s := 0

	for _, i := range integers {
		s += i
	}

	return s
}

// Kiriage returns Ceil(a/b)
// a >= 0, b > 0
func Kiriage(a, b int) int {
	return (a + (b - 1)) / b
}

// PowInt is integer version of math.Pow
// PowInt calculate a power by Binary Power (二分累乗法(O(log e))).
func PowInt(a, e int) int {
	if a < 0 || e < 0 {
		panic(errors.New("[argument error]: PowInt does not accept negative integers"))
	}

	if e == 0 {
		return 1
	}

	if e%2 == 0 {
		halfE := e / 2
		half := PowInt(a, halfE)
		return half * half
	}

	return a * PowInt(a, e-1)
}

// AbsInt is integer version of math.Abs
func AbsInt(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

// Gcd returns the Greatest Common Divisor of two natural numbers.
// Gcd only accepts two natural numbers (a, b >= 1).
// 0 or negative number causes panic.
// Gcd uses the Euclidean Algorithm.
func Gcd(a, b int) int {
	if a <= 0 || b <= 0 {
		panic(errors.New("[argument error]: Gcd only accepts two NATURAL numbers"))
	}
	if a < b {
		a, b = b, a
	}

	// Euclidean Algorithm
	for b > 0 {
		div := a % b
		a, b = b, div
	}

	return a
}

// Lcm returns the Least Common Multiple of two natural numbers.
// Lcd only accepts two natural numbers (a, b >= 1).
// 0 or negative number causes panic.
// Lcd uses the Euclidean Algorithm indirectly.
func Lcm(a, b int) int {
	if a <= 0 || b <= 0 {
		panic(errors.New("[argument error]: Gcd only accepts two NATURAL numbers"))
	}

	// a = a'*gcd, b = b'*gcd, a*b = a'*b'*gcd^2
	// a' and b' are relatively prime numbers
	// gcd consists of prime numbers, that are included in a and b
	gcd := Gcd(a, b)

	// not (a * b / gcd), because of reducing a probability of overflow
	return (a / gcd) * b
}

// Strtoi is a wrapper of `strconv.Atoi()`.
// If `strconv.Atoi()` returns an error, Strtoi calls panic.
func Strtoi(s string) int {
	if i, err := strconv.Atoi(s); err != nil {
		panic(errors.New("[argument error]: Strtoi only accepts integer string"))
	} else {
		return i
	}
}

// PrintIntsLine returns integers string delimited by a space.
func PrintIntsLine(A ...int) string {
	res := []rune{}

	for i := 0; i < len(A); i++ {
		str := strconv.Itoa(A[i])
		res = append(res, []rune(str)...)

		if i != len(A)-1 {
			res = append(res, ' ')
		}
	}

	return string(res)
}

/********** I/O usage **********/

//str := ReadString()
//i := ReadInt()
//X := ReadIntSlice(n)
//S := ReadRuneSlice()
//a := ReadFloat64()
//A := ReadFloat64Slice(n)

//str := ZeroPaddingRuneSlice(num, 32)
//str := PrintIntsLine(X...)

/*******************************************************************/

const MOD = 1000000000 + 7
const ALPHABET_NUM = 26
const INF_INT64 = math.MaxInt64
const INF_BIT60 = 1 << 60

var beki [400000 + 10]int
var sumBeki [400000 + 10]int

func main() {
	a, b, c := ReadInt3()

	ans := 0

	cf := NewCombFactorial()
	cf.InitCF()

	beki[0] = 1
	for i := 1; i < 400000+3; i++ {
		beki[i] = 2 * beki[i-1]
		beki[i] %= MOD
	}
	for i := 0; i < 400000+3; i++ {
		sumBeki[i+1] = sumBeki[i] + beki[i]
		sumBeki[i+1] %= MOD
	}

	for i := b + c - 1; i < a+b+c-1; i++ {
		m := sumBeki[i] * cf.C(i-1, c-1)
		m %= MOD
		m *= cf.C(i-c, b-1)
		m %= MOD
		ans += m
		ans %= MOD
	}

	fmt.Println(ans)
}

type CombFactorial struct {
	factorial, modFactorial [400001]int
}

func NewCombFactorial() *CombFactorial {
	cf := new(CombFactorial)

	return cf
}
func (c *CombFactorial) modInv(a int) int {
	return c.modpow(a, MOD-2)
}
func (c *CombFactorial) modpow(a, e int) int {
	if e == 0 {
		return 1
	}

	if e%2 == 0 {
		halfE := e / 2
		half := c.modpow(a, halfE)
		return half * half % MOD
	}

	return a * c.modpow(a, e-1) % MOD
}
func (c *CombFactorial) InitCF() {
	for i := 0; i <= 400000; i++ {
		if i == 0 {
			c.factorial[i] = 1
			c.modFactorial[i] = c.modInv(c.factorial[i])
			continue
		}

		num := i * c.factorial[i-1]
		num %= MOD
		c.factorial[i] = num
		c.modFactorial[i] = c.modInv(c.factorial[i])
	}
}
func (c *CombFactorial) C(n, r int) int {
	res := 1
	res *= c.factorial[n]
	res %= MOD
	res *= c.modFactorial[r]
	res %= MOD
	res *= c.modFactorial[n-r]
	res %= MOD

	return res
}
func (c *CombFactorial) P(n, r int) int {
	res := 1
	res *= c.factorial[n]
	res %= MOD
	res *= c.modFactorial[n-r]
	res %= MOD

	return res
}
func (c *CombFactorial) H(n, r int) int {
	return c.C(n-1+r, r)
}

// cf = NewCombFactorial()
// cf.InitCF()
// res := cf.C(n, r) 	// 組み合わせ
// res := cf.H(n, r) 	// 重複組合せ
// res := cf.P(n, r) 	// 順列
var cf *CombFactorial

// MODはとったか？
// 遷移だけじゃなくて最後の最後でちゃんと取れよ？

/*******************************************************************/