diff --git a/include/int2048.h b/include/int2048.h
index c7b2989..c83c521 100644
--- a/include/int2048.h
+++ b/include/int2048.h
@@ -22,6 +22,8 @@ class int2048 {
   signed char flag = +1;
   int num_length = 0;
 
+  void NTT(__int128_t *, int, int);
+
  public:
   int2048();
   int2048(long long);
diff --git a/src/int2048.cpp b/src/int2048.cpp
index 5cde16b..252a436 100644
--- a/src/int2048.cpp
+++ b/src/int2048.cpp
@@ -330,12 +330,22 @@ int2048 operator-(int2048 A, const int2048 &B) {
   return std::move(A);
 }
 
-inline void UnsignedMultiply(int2048 &A, const int2048 *pB) { ; }
+inline void UnsignedMultiply(int2048 &A, const int2048 *pB)
+{
+  ;
+}
 
 int2048 &int2048::Multiply(const int2048 &B) {
   // 实现复合乘法逻辑
   const int2048 *pB = &B;
   if (this == &B) pB = new int2048(B);
+  if ((this->num_length == 1 && this->val[0]) ||
+      (pB->num_length == 1 && pB->val[0] == 0)) {
+    *this = std::move(int2048(0));
+    return *this;
+  }
+  this->flag = this->flag * pB->flag;
+  UnsignedMultiply(*this,pB);
   return *this;
 }
 
diff --git a/tester/cases/2.py b/tester/cases/2.py
new file mode 100755
index 0000000..5f7de6d
--- /dev/null
+++ b/tester/cases/2.py
@@ -0,0 +1,85 @@
+#!/usr/bin/python3
+from os import system
+from sys import exit
+from random import randint
+"""
+this script is used to test * operator
+"""
+
+code_cpp_pre="""
+#include<iostream>
+#include "/home/happyzym/CSWorkSpace/Proc/BigHomework/BH-int2048-2023/include/int2048.h"
+using namespace std;
+using namespace sjtu;
+int main()
+{
+"""
+code_cpp_suf="""
+return 0;
+}
+"""
+def_cpp="int2048 a_0(0),a_1(0),a_2(0),a_3(0),a_4(0),a_5(0),a_6(0),a_7(0),a_8(0),a_9(0);"
+
+
+code_python_pre="""#!/usr/bin/python3
+
+"""
+def_python="a_0,a_1,a_2,a_3,a_4,a_5,a_6,a_7,a_8,a_9=0,0,0,0,0,0,0,0,0,0"
+
+
+opt_cpp=[]
+opt_python=[]
+
+if True:
+  for i in range(0,10):
+    val=randint(-2**31,2**31-1)
+    opt_cpp.append("a_"+str(i)+"="+str(val)+";")
+    opt_python.append("a_"+str(i)+"="+str(val))
+    opt_cpp.append("a_"+str(i)+".print(); puts(\"\");")
+    opt_python.append("print(a_"+str(i)+")")
+
+if True:
+  for i in range(10):
+    aid=randint(0,9)
+    bid=randint(0,9)
+    cid=randint(0,9)
+    op='*'
+    opt_cpp.append("a_"+str(aid)+"=a_"+str(bid)+op+"a_"+str(cid)+";")
+    opt_python.append("a_"+str(aid)+"=a_"+str(bid)+op+"a_"+str(cid))
+    opt_cpp.append("a_"+str(aid)+".print(); puts(\"\");")
+    opt_python.append("print(a_"+str(aid)+")")
+    opt_cpp.append("a_"+str(bid)+".print(); puts(\"\");")
+    opt_python.append("print(a_"+str(bid)+")")
+    opt_cpp.append("a_"+str(cid)+".print(); puts(\"\");")
+    opt_python.append("print(a_"+str(cid)+")")
+
+if True:
+  for i in range(10):
+    aid=randint(0,9)
+    bid=randint(0,9)
+    op='*='
+    opt_cpp.append("a_"+str(aid)+op+"a_"+str(bid)+";")
+    opt_python.append("a_"+str(aid)+op+"a_"+str(bid))
+    opt_cpp.append("a_"+str(aid)+".print(); puts(\"\");")
+    opt_python.append("print(a_"+str(aid)+")")
+
+sourc_cpp=open("/tmp/2.cpp","w")
+print(code_cpp_pre,file=sourc_cpp)
+print(def_cpp,file=sourc_cpp)
+for opt in opt_cpp:
+  print(opt,file=sourc_cpp)
+print(code_cpp_suf,file=sourc_cpp)
+sourc_cpp.close()
+system("g++ /tmp/2.cpp -I /home/happyzym/CSWorkSpace/Proc/BigHomework/BH-int2048-2023/include/ -L /home/happyzym/CSWorkSpace/Proc/BigHomework/BH-int2048-2023/build/src/ -lint2048 -o /tmp/2")
+system("/tmp/2 > /tmp/2_cpp.out")
+
+sourc_python=open("/tmp/2.py","w")
+print(code_python_pre,file=sourc_python)
+print(def_python,file=sourc_python)
+for opt in opt_python:
+  print(opt,file=sourc_python)
+sourc_python.close()
+system("chmod +x /tmp/2.py")
+system("/tmp/2.py > /tmp/2_python.out")
+
+exit(system("diff -b -B -u /tmp/2_cpp.out /tmp/2_python.out > /tmp/2.diff")//256)
\ No newline at end of file
diff --git a/tester/config.json b/tester/config.json
index 99050b6..e9f683a 100644
--- a/tester/config.json
+++ b/tester/config.json
@@ -25,6 +25,7 @@
     {"command":"timeout -s 9 10s /home/happyzym/CSWorkSpace/Proc/BigHomework/BH-int2048-2023/build/data/C2T16 >/tmp/C2T16.out && diff -b -B -u /tmp/C2T16.out /home/happyzym/CSWorkSpace/Proc/BigHomework/BH-int2048-2023/data/Integer2/16.out >/tmp/diffC2T16","uid":"#26","tid":"/2/16"},
     {"command":"timeout -s 9 10s /home/happyzym/CSWorkSpace/Proc/BigHomework/BH-int2048-2023/build/data/C2T17 >/tmp/C2T17.out && diff -b -B -u /tmp/C2T17.out /home/happyzym/CSWorkSpace/Proc/BigHomework/BH-int2048-2023/data/Integer2/17.out >/tmp/diffC2T17","uid":"#27","tid":"/2/17"},
     {"command":"timeout -s 9 10s /home/happyzym/CSWorkSpace/Proc/BigHomework/BH-int2048-2023/build/data/C2T18 >/tmp/C2T18.out && diff -b -B -u /tmp/C2T18.out /home/happyzym/CSWorkSpace/Proc/BigHomework/BH-int2048-2023/data/Integer2/18.out >/tmp/diffC2T18","uid":"#28","tid":"/2/18"},
-    {"command":"/home/happyzym/CSWorkSpace/Proc/BigHomework/BH-int2048-2023/tester/cases/1.py","uid":"#29","tid":"/3/1"}
+    {"command":"/home/happyzym/CSWorkSpace/Proc/BigHomework/BH-int2048-2023/tester/cases/1.py","uid":"#29","tid":"/3/1"},
+    {"command":"/home/happyzym/CSWorkSpace/Proc/BigHomework/BH-int2048-2023/tester/cases/2.py","uid":"#30","tid":"/3/2"}
   ]
 }
\ No newline at end of file