Problem:
Score : 100 points

Problem Statement

Find the number of integers between 1 and K (inclusive) satisfying the following condition, modulo 10^9 + 7:

The sum of the digits in base ten is a multiple of D.

Constraints

All values in input are integers.

1 \leq K < 10^{10000}

1 \leq D \leq 100

Input

Input is given from Standard Input in the following format:

K
D

Output

Print the number of integers satisfying the condition, modulo 10^9 + 7.

Sample Input 1

30
4

Sample Output 1

6

Those six integers are: 4, 8, 13, 17, 22 and 26.

Sample Input 2

1000000009
1

Sample Output 2

2

Be sure to print the number modulo 10^9 + 7.

Sample Input 3

98765432109876543210
58

Sample Output 3

635270834

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

def get_i() #空白区切の入力を数値(整数)の配列で返す
  return gets.chomp.split(" ").map(&:to_i)
end
def get_f() #空白区切の入力を数値(実数)の配列で返す
  return gets.chomp.split(" ").map(&:to_f)
end
def get() #空白区切の入力を文字列の配列で返す
  return gets.chomp.split(" ")
end
def get_nsp() #入力されたものを一文字ずつに区切った文字列の配列で返す
  return gets.chomp.split("")
end
def yn_judge(bool,y="Yes",n="No") #boolに真偽を投げることで、trueならy、falseならnの値を出力する
  return bool ? y : n 
end
def array(size1,init=nil,size2=1) #size2に二次元配列時の最初の要素数、size1に次の配列の大きさ、initに初期値を投げることでその配列を返す
  if size2==1
    return Array.new(size1){init}
  else
    return Array.new(size2){Array.new(size1){init}}
  end
end

K=get_nsp.map(&:to_i)
D=gets.to_i
L=K.size
dp=Array.new(L+1){Array.new(2){Array.new(D){0}}}

dp[0][0][0]=1
MOD=1000_000_007
L.times do|i|
  dp_current,dp_next=dp[i],dp[i+1]
  dp_current_0,dp_current_1=dp_current[0],dp_current[1]
  dp_next_0,dp_next_1=dp_next[0],dp_next[1]
  D.times do|j|
    10.times do|k|
      dp_next_1[(k+j)%D]+=dp_current_1[j]
      dp_next_1[(k+j)%D]%=MOD
    end 
    K[i].times do|k|
      dp_next_1[(k+j)%D]+=dp_current_0[j]
      dp_next_1[(k+j)%D]%=MOD
    end
    dp_next_0[(j+K[i])%D]=dp_current_0[j]
  end
end
puts dp[L][0][0]+dp[L][1][0]-1